All Outputs (65)

Phase and amplitude responses for delay equations using harmonic balance (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Phase and amplitude responses for delay equations using harmonic balance. Physical Review E, 110(1), Article L012202. https://doi.org/10.1103/PhysRevE.110.L012202

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a gr... Read More about Phase and amplitude responses for delay equations using harmonic balance.

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.

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.

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.

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.

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.

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.

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

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.