Outputs (87)

Stability analysis of electrical microgrids and their control systems (2024)
Journal Article
Smith, O., Coombes, S., & O'Dea, R. D. (2024). Stability analysis of electrical microgrids and their control systems. PRX Energy, 3(1), Article 013011. https://doi.org/10.1103/PRXEnergy.3.013011

The drive towards renewable energy generation is causing fundamental changes in both the structure and dynamics of power grids. Their topology is becoming increasingly decentralised due to distributed, embedded generation, and the emergence of microg... Read More about Stability analysis of electrical microgrids and their control systems.

Insights into oscillator network dynamics using a phase-isostable framework (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Insights into oscillator network dynamics using a phase-isostable framework. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1), Article 013141. https://doi.org/10.1063/5.0179430

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolu... Read More about Insights into oscillator network dynamics using a phase-isostable framework.

Understanding the effect of white matter delays on large scale brain synchrony (2024)
Journal Article
Şaylı, M., & Coombes, S. (2024). Understanding the effect of white matter delays on large scale brain synchrony. Communications in Nonlinear Science and Numerical Simulation, 131, Article 107803. https://doi.org/10.1016/j.cnsns.2023.107803

The presence of myelin is a powerful structural factor that controls the conduction speed of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the majo... Read More about Understanding the effect of white matter delays on large scale brain synchrony.

Next generation neural population models (2023)
Journal Article
Coombes, S. (2023). Next generation neural population models. Frontiers in Applied Mathematics and Statistics, 9, Article 112822. https://doi.org/10.3389/fams.2023.1128224

Low-dimensional neural mass models are often invoked to model the coarse-grained activity of large populations of neurons and synapses and have been used to help understand the coordination of large scale brain rhythms. However, they are phenomenolog... Read More about Next generation neural population models.

The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective (2022)
Journal Article
Şaylı, M., Skeldon, A. C., Thul, R., Nicks, R., & Coombes, S. (2023). The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective. Physica D: Nonlinear Phenomena, 444, Article 133595. https://doi.org/10.1016/j.physd.2022.133595

Since its inception four decades ago the two-process model introduced by Borbély has provided the conceptual framework to explain sleep–wake regulation across many species, including humans. At its core, high level notions of circadian and homeostati... Read More about The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective.

Structure-function clustering in weighted brain networks (2022)
Journal Article
Crofts, J. J., Forrester, M., Coombes, S., & O’Dea, R. D. (2022). Structure-function clustering in weighted brain networks. Scientific Reports, 12(1), Article 16793. https://doi.org/10.1038/s41598-022-19994-9

Functional networks, which typically describe patterns of activity taking place across the cerebral cortex, are widely studied in neuroscience. The dynamical features of these networks, and in particular their deviation from the relatively static str... Read More about Structure-function clustering in weighted brain networks.

Neural fields with rebound currents: Novel routes to patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural fields with rebound currents: Novel routes to patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. Replicating this success for subcortical tissues, such as the thalamus, r... Read More about Neural fields with rebound currents: Novel routes to patterning.

Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models (2021)
Journal Article
Tewarie, P., Prasse, B., Meier, J. M., Byrne, Á., De Domenico, M., Stam, C. J. (., …Van Mieghem, P. (2021). Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models. New Journal of Physics, 23(6), Article 063065. https://doi.org/10.1088/1367-2630/ac066d

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat... Read More about Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models.

Mean-Field Models for EEG/MEG: From Oscillations to Waves (2021)
Journal Article
Byrne, Á., Ross, J., Nicks, R., & Coombes, S. (2022). Mean-Field Models for EEG/MEG: From Oscillations to Waves. Brain Topography, 35, 36–53. https://doi.org/10.1007/s10548-021-00842-4

Neural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological consideration... Read More about Mean-Field Models for EEG/MEG: From Oscillations to Waves.

Understanding sensory induced hallucinations: From neural fields to amplitude equations (2021)
Journal Article
Nicks, R., Cocks, A., Avitabile, D., Johnston, A., & Coombes, S. (2021). Understanding sensory induced hallucinations: From neural fields to amplitude equations. SIAM Journal on Applied Dynamical Systems, 20(4), 1683-1714. https://doi.org/10.1137/20M1366885

Explorations of visual hallucinations, and in particular those of Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490-8495], show that annular rings with a background flicker can induce visual hallucinatio... Read More about Understanding sensory induced hallucinations: From neural fields to amplitude equations.

Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation (2021)
Journal Article
Bast, T., Coombes, S., O’Dea, R., & Tessereau, C. (2021). Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation. Brain and Neuroscience Advances, 5, https://doi.org/10.1177/2398212820975634

Humans and non-human animals show great flexibility in spatial navigation, including the ability to return to specific locations based on as few as one single experience. To study spatial navigation in the laboratory, watermaze tasks, in which rats h... Read More about Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation.

Neural Fields with Rebound Currents: Novel Routes to Patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural Fields with Rebound Currents: Novel Routes to Patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. To replicate this success for sub-cortical tissues, such as the thalamus,... Read More about Neural Fields with Rebound Currents: Novel Routes to Patterning.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain (2020)
Journal Article
Forrester, M., Crofts, J. J., Sotiropoulos, S. N., Coombes, S., & O'Dea, R. D. (2020). The role of node dynamics in shaping emergent functional connectivity patterns in the brain. Network Neuroscience, 4(2), 467-483. https://doi.org/10.1162/netn_a_00130

© 2020 Massachusetts Institute of Technology. The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating... Read More about The role of node dynamics in shaping emergent functional connectivity patterns in the brain.

Quasicrystal patterns in a neural field model (2020)
Journal Article
Gökçe, A., Coombes, S., & Avitabile, D. (2020). Quasicrystal patterns in a neural field model. Physical Review Research, 2(1), Article 013234. https://doi.org/10.1103/PhysRevResearch.2.013234

Doubly periodic patterns in planar neural field models have been extensively studied since the 1970s for their role in explaining geometric visual hallucinations. The study of activity patterns that lack translation invariance has received little, if... Read More about Quasicrystal patterns in a neural field model.

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans (2020)
Journal Article
Lai, Y. M., Coombes, S., & Thul, R. (2020). Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans. Communications in Nonlinear Science and Numerical Simulation, 85, Article 105181. https://doi.org/10.1016/j.cnsns.2020.105181

In cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous p... Read More about Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans.

Brain-wave equation incorporating axodendritic connectivity (2020)
Journal Article
Ross, J., Margetts, M., Bojak, I., Nicks, R., Avitabile, D., & Coombes, S. (2020). Brain-wave equation incorporating axodendritic connectivity. Physical Review E, 101(2), Article 022411. https://doi.org/10.1103/PhysRevE.101.022411

©2020 American Physical Society. We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natu... Read More about Brain-wave equation incorporating axodendritic connectivity.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain (2020)
Journal Article
Forrester, M., Crofts, J. J., Sotiropoulos, S., Coombes, S., & O’Dea, R. (2020). The role of node dynamics in shaping emergent functional connectivity patterns in the brain. Network Neuroscience, 4(2), 467-483. https://doi.org/10.1162/netn_a_00130

The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating a system of Jansen–Rit neural-mass nodes with... Read More about The role of node dynamics in shaping emergent functional connectivity patterns in the brain.

Next-generation neural mass and field modeling (2019)
Journal Article
Byrne, Á., O’Dea, R. D., Coombes, S., Forrester, M., & Ross, J. (2020). Next-generation neural mass and field modeling. Journal of Neurophysiology, 123(2), 726-742. https://doi.org/10.1152/jn.00406.2019

The Wilson-Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained f... Read More about Next-generation neural mass and field modeling.

A master stability function approach to cardiac alternans (2019)
Journal Article
Lai, Y. M., Veasy, J., Coombes, S., & Thul, R. (2019). A master stability function approach to cardiac alternans. Applied Network Science, 4(1), https://doi.org/10.1007/s41109-019-0199-z

During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a varie... Read More about A master stability function approach to cardiac alternans.

Synchrony in networks of Franklin bells (2019)
Journal Article
Sayli, M., Lai, Y. M., Thul, R., & Coombes, S. (2019). Synchrony in networks of Franklin bells. IMA Journal of Applied Mathematics, 84(5), 1001-1021. https://doi.org/10.1093/imamat/hxz023

The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal be... Read More about Synchrony in networks of Franklin bells.

Complex patterns of subcellular cardiac alternans (2019)
Journal Article
Veasy, J., Lai, Y. M., Coombes, S., & Thul, R. (2019). Complex patterns of subcellular cardiac alternans. Journal of Theoretical Biology, 478, 102-114. https://doi.org/10.1016/j.jtbi.2019.06.016

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A... Read More about Complex patterns of subcellular cardiac alternans.

Next-generation neural field model: The evolution of synchrony within patterns and waves (2019)
Journal Article
Byrne, Á., Avitabile, D., & Coombes, S. (2019). Next-generation neural field model: The evolution of synchrony within patterns and waves. Physical Review E, 99(1), Article 012313. https://doi.org/10.1103/physreve.99.012313

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue... Read More about Next-generation neural field model: The evolution of synchrony within patterns and waves.

How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes (2018)
Journal Article
Tewarie, P., Abeysuriya, R., Byrne, Á., O'Neill, G. C., Sotiropoulos, S. N., Brookes, M. J., & Coombes, S. (2019). How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes. NeuroImage, 186, 211-220. https://doi.org/10.1016/j.neuroimage.2018.10.079

Functional networks obtained from magnetoencephalography (MEG) from different frequency bands show distinct spatial patterns. It remains to be elucidated how distinct spatial patterns in MEG networks emerge given a single underlying structural networ... Read More about How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes.

Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony (2018)
Journal Article
Yi Ming, L., Thul, R., & Coombes, S. (2018). Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony. European Physical Journal - Special Topics, 227(10-11), 1251-1265. https://doi.org/10.1140/epjst/e2018-800033-y

Integrate-and-fire networks have proven remarkably useful in modelling the dynamics of real world phenomena ranging from earthquakes, to synchrony in neural networks, to cascading activity in social networks. The reset process means that such models... Read More about Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony.

Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity (2018)
Journal Article
Tewarie, P., Hunt, B. A. E., O'Neill, G. C., Byrne, A., Aquino, K., Bauer, M., …Brookes, M. J. (2018). Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity. Cerebral Cortex, 29(6), 2668-2681. https://doi.org/10.1093/cercor/bhy136

Event related fluctuations of neural oscillatory amplitude are reported widely in the context of cognitive processing and are typically interpreted as a marker of brain ‘activity’. However, the precise nature of these effects remains unclear; in part... Read More about Relationships Between Neuronal Oscillatory Amplitude and Dynamic Functional Connectivity.

Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals (2018)
Journal Article
McIvor, E., Coombes, S., & Thul, R. (2018). Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals. Cell Calcium, 73, https://doi.org/10.1016/j.ceca.2018.03.006

The spatial organisation of Orai channels and SERCA pumps within ER-PM junctions is important for enhancing the versatility and specificity of subcellular Ca2+ signals generated during store operated Ca2+ entry (SOCE). In this paper we present a nove... Read More about Three-dimensional spatio-temporal modelling of store operated Ca2+ entry: insights into ER refilling and the spatial signature of Ca2+ signals.

Clusters in nonsmooth oscillator networks (2018)
Journal Article
Nicks, R., Chambon, L., & Coombes, S. (2018). Clusters in nonsmooth oscillator networks. Physical Review E, 97(3), Article 032213. https://doi.org/10.1103/PhysRevE.97.032213

© 2018 American Physical Society. For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory... Read More about Clusters in nonsmooth oscillator networks.

Neural Fields: Localised States with Piece-Wise Constant Interactions (2018)
Book Chapter
Gökçe, A., Coombes, S., & Avitabile, D. (2018). Neural Fields: Localised States with Piece-Wise Constant Interactions. In Mathematical and Theoretical Neuroscience: Cell, Network and Data Analysis (111-121). Cham, Switzerland: Springer Nature. https://doi.org/10.1007/978-3-319-68297-6_7

Neural field models are typically cast as continuum integro-differential equations for describing the idealised coarse-grained activity of populations of interacting neurons. For smooth Mexican hat kernels, with short-range excitation and long-range... Read More about Neural Fields: Localised States with Piece-Wise Constant Interactions.

Networks of piecewise linear neural mass models (2018)
Journal Article
Coombes, S., Lai, Y. M., Sayli, M., & Thul, R. (2018). Networks of piecewise linear neural mass models. European Journal of Applied Mathematics, 29(Special issue 5), 869-890. https://doi.org/10.1017/S0956792518000050

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ordinary differential equations with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlase... Read More about Networks of piecewise linear neural mass models.

The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions (2017)
Journal Article
Gökçe, A., Avitabile, D., & Coombes, S. (2017). The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions. Journal of Mathematical Neuroscience, 7(1), Article 12. https://doi.org/10.1186/s13408-017-0054-4

© 2017, The Author(s). Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounde... Read More about The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions.

An analysis of waves underlying grid cell firing in the medial enthorinal cortex (2017)
Journal Article
Bonilla-Quintana, M., Wedgwood, K. C., O'Dea, R. D., & Coombes, S. (in press). An analysis of waves underlying grid cell firing in the medial enthorinal cortex. Journal of Mathematical Neuroscience, 7(9), https://doi.org/10.1186/s13408-017-0051-7

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational... Read More about An analysis of waves underlying grid cell firing in the medial enthorinal cortex.

A mean field model for movement induced changes in the beta rhythm (2017)
Journal Article
Byrne, Á., Brookes, M. J., & Coombes, S. (2017). A mean field model for movement induced changes in the beta rhythm. Journal of Computational Neuroscience, 43(2), https://doi.org/10.1007/s10827-017-0655-7

In electrophysiological recordings of the brain, the transition from high amplitude to low amplitude signals are most likely caused by a change in the synchrony of underlying neuronal population firing patterns. Classic examples of such modulations... Read More about A mean field model for movement induced changes in the beta rhythm.

Standing and travelling waves in a spherical brain model: the Nunez model revisited (2017)
Journal Article
Visser, S., Nicks, R., Faugeras, O., & Coombes, S. (2017). Standing and travelling waves in a spherical brain model: the Nunez model revisited. Physica D: Nonlinear Phenomena, 349, https://doi.org/10.1016/j.physd.2017.02.017

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or... Read More about Standing and travelling waves in a spherical brain model: the Nunez model revisited.

Combining spatial and parametric working memory in a dynamic neural field model (2016)
Journal Article
Wojtak, W., Coombes, S., Bicho, E., & Erlhagen, W. (in press). Combining spatial and parametric working memory in a dynamic neural field model. Lecture Notes in Artificial Intelligence, 9886, https://doi.org/10.1007/978-3-319-44778-0_48

We present a novel dynamic neural field model consisting of two coupled fields of Amari-type which supports the existence of localized activity patterns or “bumps” with a continuum of amplitudes. Bump solutions have been used in the past to model spa... Read More about Combining spatial and parametric working memory in a dynamic neural field model.

Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function (2016)
Journal Article
Coombes, S., & Thul, R. (2016). Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, 27(6), 904-922. https://doi.org/10.1017/S0956792516000115

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbi... Read More about Synchrony in networks of coupled nonsmooth dynamical systems: extending the master stability function.

Neural field models with threshold noise (2016)
Journal Article
Thul, R., Coombes, S., & Laing, C. R. (2016). Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6, Article 3. https://doi.org/10.1186/s13408-016-0035-z

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate funct... Read More about Neural field models with threshold noise.

Mathematical frameworks for oscillatory network dynamics in neuroscience (2016)
Journal Article
Ashwin, P., Coombes, S., & Nicks, R. (2016). Mathematical frameworks for oscillatory network dynamics in neuroscience. Journal of Mathematical Neuroscience, 6, Article 2. https://doi.org/10.1186/s13408-015-0033-6

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting nov... Read More about Mathematical frameworks for oscillatory network dynamics in neuroscience.

Mathematical neuroscience: from neurons to networks (2015)
Book Chapter
Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. T... Read More about Mathematical neuroscience: from neurons to networks.

Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes (2015)
Journal Article
Thul, R., Rietdorf, K., Bootman, M. D., & Coombes, S. (2015). Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1853(9), https://doi.org/10.1016/j.bbamcr.2015.02.019

Atrial myocytes in a number of species lack transverse tubules. As a consequence the intracellular calcium signals occurring during each heartbeat exhibit complex spatio-temporal dynamics. These calcium patterns arise from saltatory calcium waves tha... Read More about Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes.

Spots: breathing, drifting and scattering in a neural field model (2014)
Book Chapter
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In S. Coombs, P. Beim Graben, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applications (187-211). Springer. https://doi.org/10.1007/978-3-642-54593-1_7

Two dimensional neural field models with short range excitation and long range inhibition can exhibit localised solutions in the form of spots. Moreover, with the inclusion of a spike frequency adaptation current, these models can also support breath... Read More about Spots: breathing, drifting and scattering in a neural field model.

Travelling waves in models of neural tissue: from localised structures to periodic waves (2014)
Journal Article
Meijer, H., & Coombes, S. (2014). Travelling waves in models of neural tissue: from localised structures to periodic waves. EPJ Nonlinear Biomedical Physics, 2(3), https://doi.org/10.1140/epjnbp16

We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti... Read More about Travelling waves in models of neural tissue: from localised structures to periodic waves.

Travelling waves in a neural field model with refractoriness (2013)
Journal Article
Meijer, H. G., & Coombes, S. (2014). Travelling waves in a neural field model with refractoriness. Journal of Mathematical Biology, 68(5), 1249-1268. https://doi.org/10.1007/s00285-013-0670-x

At one level of abstraction neural tissue can be regarded as a medium for turning local synaptic activity into output signals that propagate over large distances via axons to generate further synaptic activity that can cause reverberant activity in n... Read More about Travelling waves in a neural field model with refractoriness.

A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition (2013)
Journal Article
Zachariou, M., Alexander, S. P., Coombes, S., & Christodoulou, C. (2013). A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition. PLoS ONE, 8(3), Article e58296. https://doi.org/10.1371/journal.pone.0058926

Memories are believed to be represented in the synaptic pathways of vastly interconnected networks of neurons. The plasticity of synapses, that is, their strengthening and weakening depending on neuronal activity, is believed to be the basis of lea... Read More about A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition.

Limitations of perturbative techniques in the analysis of rhythms and oscillations (2013)
Journal Article
Lin, K. K., Wedgwood, K. C., Coombes, S., & Young, L. (2013). Limitations of perturbative techniques in the analysis of rhythms and oscillations. Journal of Mathematical Biology, 66(1-2), https://doi.org/10.1007/s00285-012-0506-0

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when... Read More about Limitations of perturbative techniques in the analysis of rhythms and oscillations.

Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves (2012)
Journal Article
Thul, R., Coombes, S., & Bootman, M. D. (2012). Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves. Frontiers in Physiology, 3, Article 279. https://doi.org/10.3389/fphys.2012.00279

Clusters of ryanodine receptors within atrial myocytes are confined to spatially separated layers. In many species, these layers are not juxtaposed by invaginations of the plasma membrane (transverse tubules; 'T-tubules'), so that calcium-induced-cal... Read More about Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves.

Interface dynamics in planar neural field models (2012)
Journal Article
Coombes, S., Schmidt, H., & Bojak, I. (2012). Interface dynamics in planar neural field models. Journal of Mathematical Neuroscience, 2(1), 1-46. https://doi.org/10.1186/2190-8567-2-9

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patt... Read More about Interface dynamics in planar neural field models.

Using evolutionary algorithms for fitting high-dimensional models to neuronal data (2012)
Journal Article
Svensson, C., Coombes, S., & Peirce, J. (2012). Using evolutionary algorithms for fitting high-dimensional models to neuronal data. Neuroinformatics, 10(2), https://doi.org/10.1007/s12021-012-9140-7

n the study of neurosciences, and of complex biological systems in general, there is frequently a need to fit mathematical models with large numbers of parameters to highly complex datasets. Here we consider algorithms of two different classes, gradi... Read More about Using evolutionary algorithms for fitting high-dimensional models to neuronal data.

Neuronal spike-train responses in the presence of threshold noise (2012)
Journal Article
Coombes, S., Thul, R., Laudanski, J., Palmer, A., & Sumner, C. (in press). Neuronal spike-train responses in the presence of threshold noise. Frontiers in Life Science, 5(3-4), https://doi.org/10.1080/21553769.2011.556016

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent chan... Read More about Neuronal spike-train responses in the presence of threshold noise.

Subcellular calcium dynamics in a whole-cell model of an atrial myocyte (2012)
Journal Article
Thul, R., Coombes, S., Roderick, H. L., & Bootman, M. D. (2012). Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proceedings of the National Academy of Sciences, 109(6), 2150-2155. https://doi.org/10.1073/pnas.1115855109

In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca 2+ movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic re... Read More about Subcellular calcium dynamics in a whole-cell model of an atrial myocyte.

Nonsmooth dynamics in spiking neuron models (2011)
Journal Article
Coombes, S., Thul, R., & Wedgwood, K. C. (2012). Nonsmooth dynamics in spiking neuron models. Physica D: Nonlinear Phenomena, 241(22), https://doi.org/10.1016/j.physd.2011.05.012

Large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue. One approach in computational neuroscience has been to consider the detailed electrophysiological propertie... Read More about Nonsmooth dynamics in spiking neuron models.

Pulsating fronts in periodically modulated neural field models (2011)
Journal Article
Coombes, S., & Laing, C. (in press). Pulsating fronts in periodically modulated neural field models. Physical Review E, Article 011912. https://doi.org/10.1103/PhysRevE.83.011912

We consider a coarse grained neural field model for synaptic activity in spatially extended cortical tissue that possesses an underlying periodicity in its microstructure. The model is written as an integro-differential equation with periodic modula... Read More about Pulsating fronts in periodically modulated neural field models.

Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article
Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: Approximate solutions. Discrete and Continuous Dynamical Systems - Series A, 28(4), 1369-1379. https://doi.org/10.3934/dcds.2010.28.1369

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article
Hlinka, J., Hlinka, J., & Coombes, S. (2010). Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks. Physical Review Letters, 104(6), https://doi.org/10.1103/PhysRevLett.104.068101

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article
Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52(3), 731-739. https://doi.org/10.1016/j.neuroimage.2010.01.045

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

Understanding cardiac alternans: a piecewise linear modeling framework (2010)
Journal Article
Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20, https://doi.org/10.1063/1.3518362

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca²⁺) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of the... Read More about Understanding cardiac alternans: a piecewise linear modeling framework.

Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map (2010)
Journal Article
Laudanski, J., Sumner, C., & Coombes, S. (2010). Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map. Physical Review E, 82(1), Article e011924. https://doi.org/10.1103/PhysRevE.82.011924

Thalamocortical (TC) neurones are known to express the low-voltage activated, inactivating Ca2+ current IT. The triggering of this current underlies the generation of low threshold Ca2+ potentials that may evoke single or bursts of action potentials.... Read More about Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map.

Mathematical Modeling of Glucose Homeostasis and Its Relationship With Energy Balance and Body Fat (2009)
Journal Article
Smith, J. M., Maas, J. A., Garnsworthy, P. C., Owen, M. R., Coombes, S., Pillay, T. S., …Symonds, M. E. (2009). Mathematical Modeling of Glucose Homeostasis and Its Relationship With Energy Balance and Body Fat. Obesity, 17(4), 632-639. https://doi.org/10.1038/oby.2008.604

Delays in activity-based neural networks (2009)
Journal Article
Coombes, S., & Laing, C. (2009). Delays in activity-based neural networks. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 367(1891), 1117-1129. https://doi.org/10.1098/rsta.2008.0256

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discu... Read More about Delays in activity-based neural networks.

Mode locking in a spatially extended neuron model: Active soma and compartmental tree (2009)
Journal Article
Svensson, C. M., Svensson, C., & Coombes, S. (2009). Mode locking in a spatially extended neuron model: Active soma and compartmental tree. International Journal of Bifurcation and Chaos, 19(8), 2597-2607. https://doi.org/10.1142/S0218127409024347

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example, it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a c... Read More about Mode locking in a spatially extended neuron model: Active soma and compartmental tree.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics (2009)
Journal Article
Thul, R., Coombes, S., & Smith, G. (2009). Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D: Nonlinear Phenomena, 238, https://doi.org/10.1016/j.physd.2009.08.011

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitl... Read More about Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics.

Gap Junctions and Emergent Rhythms (2009)
Book Chapter
Coombes, S., & Zachariou, M. (2009). Gap Junctions and Emergent Rhythms. In J. Rubin, K. Josic, M. Matias, & R. Romo (Eds.), Coherent Behavior in Neuronal Networks. Springer

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic ne... Read More about Gap Junctions and Emergent Rhythms.

Instabilities in threshold-diffusion equations with delay (2008)
Journal Article
Laing, C. R., & Coombes, S. (2009). Instabilities in threshold-diffusion equations with delay. Physica D: Nonlinear Phenomena, 238(3), 264-272. https://doi.org/10.1016/j.physd.2008.10.014

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scal... Read More about Instabilities in threshold-diffusion equations with delay.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models (2008)
Journal Article
Coombes, S. (2008). Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models. SIAM Journal on Applied Dynamical Systems, 7(3), 1101–1129. https://doi.org/10.1137/070707579

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of the... Read More about Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models.

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis (2008)
Journal Article
Zachariou, M., Dissanayake, D. W. N., Coombes, S., Owen, M. R., & Mason, R. (in press). Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis. Cognitive Neurodynamics, 2, https://doi.org/10.1007/s11571-008-9050-4

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific... Read More about Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis.

Democratization in a passive dendritic tree: An analytical investigation (2008)
Journal Article
Timofeeva, Y., Cox, S. J., Coombes, S., & Josic, K. (2008). Democratization in a passive dendritic tree: An analytical investigation. Journal of Computational Neuroscience, 25(2), 228-244. https://doi.org/10.1007/s10827-008-0075-9

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democr... Read More about Democratization in a passive dendritic tree: An analytical investigation.

Modeling electrocortical activity through improved local approximations of integral neural field equations (2007)
Journal Article
Coombes, S., Venkov, N., Shiau, L., Bojak, I., Liley, D., & Laing, C. (2007). Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76(5), https://doi.org/10.1103/PhysRevE.76.051901

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equatio... Read More about Modeling electrocortical activity through improved local approximations of integral neural field equations.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities (2007)
Journal Article
Owen, M. R., Laing, C., & Coombes, S. (2007). Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9(378), https://doi.org/10.1088/1367-2630/9/10/378

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model... Read More about Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities.

A bidomain threshold model of propagating calcium waves (2007)
Journal Article
Thul, R., Smith, G., & Coombes, S. (2008). A bidomain threshold model of propagating calcium waves. Journal of Mathematical Biology, 56(4), https://doi.org/10.1007/s00285-007-0123-5

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travell... Read More about A bidomain threshold model of propagating calcium waves.

Dynamic instabilities in scalar neural field equations with space-dependent delays (2007)
Journal Article
Venkov, N. A., Coombes, S., & Matthews, P. C. (2007). Dynamic instabilities in scalar neural field equations with space-dependent delays. Physica D: Nonlinear Phenomena, 232(1), 1-15. https://doi.org/10.1016/j.physd.2007.04.011

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynam... Read More about Dynamic instabilities in scalar neural field equations with space-dependent delays.

Branching dendrites with resonant membrane: a "sum-over-trips" approach (2007)
Journal Article
Coombes, S., Timofeeva, Y., Svennson, C., Lord, G., Josic, K., Cox, S. J., & Colbert, C. (2007). Branching dendrites with resonant membrane: a "sum-over-trips" approach. Biological Cybernetics, 97(2), https://doi.org/10.1007/s00422-007-0161-5

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dend... Read More about Branching dendrites with resonant membrane: a "sum-over-trips" approach.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation (2007)
Journal Article
Coombes, S., & Owen, M. R. (2007). Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognize... Read More about Exotic dynamics in a firing rate model of neural tissue with threshold accommodation.

Calcium oscillations (2007)
Book Chapter
Thul, R., Bellamy, T., Roderick, L., Bootman, M., & Coombes, S. (2007). Calcium oscillations. In M. Maroto, & N. Monk (Eds.), Cellular Oscillatory Mechanisms. Springer

Changes in cellular calcium concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Calcium can also trigger cell death throu... Read More about Calcium oscillations.

The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study (2006)
Journal Article
Zachariou, M., Dissanayake, D., Owen, M. R., Mason, R., & Coombes, S. The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study. Neurocomputing, 70(10/12), https://doi.org/10.1016/j.neucom.2006.10.065

Gating of sensory (e.g. auditory) information has been demonstrated as a reduction in the auditory-evoked potential responses recorded in the brain of both normal animals and human subjects. Auditory gating is perturbed in schizophrenic patients and... Read More about The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study.

Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework (2006)
Journal Article
Timofeeva, Y., Lord, G., & Coombes, S. (2006). Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework. Journal of Computational Neuroscience, 21(3), 293-306. https://doi.org/10.1007/s10827-006-8776-4

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In th... Read More about Spatio-temporal filtering properties of a dendritic cable with active spines: A modeling study in the spike-diffuse-spike framework.

Mode locking in a periodically forced "ghostbursting" neuron model (2005)
Journal Article
Laing, C. R., & Coombes, S. (2005). Mode locking in a periodically forced "ghostbursting" neuron model. International Journal of Bifurcation and Chaos, 15(4), 1433-1444. https://doi.org/10.1142/S0218127405012557

We study a minimal integrate-and-fire based model of a " ghostbursting" neuron under periodic stimulation. These neurons are involved in sensory processing in weakly electric fish. There exist regions in parameter space in which the model neuron is m... Read More about Mode locking in a periodically forced "ghostbursting" neuron model.

Bumps, breathers, and waves in a neural network with spike frequency adaptation (2005)
Journal Article
Coombes, S., & Owen, M. R. (2005). Bumps, breathers, and waves in a neural network with spike frequency adaptation. Physical Review Letters, 94(14), https://doi.org/10.1103/PhysRevLett.94.148102

In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon the non-local network connectivity... Read More about Bumps, breathers, and waves in a neural network with spike frequency adaptation.

Directed percolation in a two dimensional stochastic fire-diffuse-fire model (2004)
Journal Article
Timofeeva, Y., & Coombes, S. (2004). Directed percolation in a two dimensional stochastic fire-diffuse-fire model

In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release th... Read More about Directed percolation in a two dimensional stochastic fire-diffuse-fire model.

Evans functions for integral neural field equations with Heaviside firing rate function (2004)
Journal Article
Coombes, S., & Owen, M. R. Evans functions for integral neural field equations with Heaviside firing rate function. SIAM Journal on Applied Dynamical Systems, 3(4), https://doi.org/10.1137/040605953

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of syste... Read More about Evans functions for integral neural field equations with Heaviside firing rate function.

Existence and wandering of bumps in a spiking neural network model
Journal Article
Chow, C., & Coombes, S. (2006). Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to tho... Read More about Existence and wandering of bumps in a spiking neural network model.

Phase-amplitude descriptions of neural oscillator models
Journal Article
Wedgwood, K. C., Lin, K. K., Thul, R., & Coombes, S. Phase-amplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3(2), https://doi.org/10.1186/2190-8567-3-2

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well... Read More about Phase-amplitude descriptions of neural oscillator models.

Using computational models to relate structural and functional brain connectivity
Journal Article
Hlinka, J., & Coombes, S. Using computational models to relate structural and functional brain connectivity. European Journal of Neuroscience, 36(2), https://doi.org/10.1111/j.1460-9568.2012.08081.x

Modern imaging methods allow a non-invasive assessment of both structural and functional brain connectivity. This has lead to the identification of disease-related alterations affecting functional connectivity. The mechanism of how such alterations... Read More about Using computational models to relate structural and functional brain connectivity.

Toward blueprints for network architecture, biophysical dynamics, and signal transduction
Journal Article
Coombes, S., Doiron, B., Josic, K., & Shea-Brown, E. (2006). Toward blueprints for network architecture, biophysical dynamics, and signal transduction

We review mathematical aspects of biophysical dynamics, signal transduction and network architecture that have been used to uncover functionally significant relations between the dynamics of single neurons and the networks they compose. We focus on... Read More about Toward blueprints for network architecture, biophysical dynamics, and signal transduction.

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release
Journal Article
Coombes, S., Hinch, R., & Timofeeva, Y. (2004). Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochasti... Read More about Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release.

Clustering through post inhibitory rebound in synaptically coupled neurons
Journal Article
Chik, D. T. W., Coombes, S., & Wang, Z. D. (2004). Clustering through post inhibitory rebound in synaptically coupled neurons

Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before returning to rest. It is an important mechanism u... Read More about Clustering through post inhibitory rebound in synaptically coupled neurons.

Waves, bumps, and patterns in neural field theories
Journal Article
Coombes, S. (2005). Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nat... Read More about Waves, bumps, and patterns in neural field theories.

Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework
Journal Article
Timofeeva, Y., Lord, G., & Coombes, S. (2005). Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Her... Read More about Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework.

The importance of different timings of excitatory and inhibitory pathways in neural field models
Journal Article
Laing, C., & Coombes, S. (2005). The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using... Read More about The importance of different timings of excitatory and inhibitory pathways in neural field models.