Research Repository

See what's under the surface


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), doi: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

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. doi: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

Relationships between neuronal oscillatory amplitude and dynamic functional connectivity (2018)
Journal Article
Tewarie, P. K., Hunt, B. A. E., O'Neill, G. C., Byrne, A., Aquino, K., Bauer, M., …Brookes, M. J. (in press). Relationships between neuronal oscillatory amplitude and dynamic functional connectivity. Cerebral Cortex, doi:10.1093/cercor/bhy136. ISSN 1047-3211

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

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, doi:10.1016/j.ceca.2018.03.006. ISSN 0143-4160

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

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 AnalysisSpringer Nature. doi: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

Networks of piecewise linear neural mass models (2018)
Journal Article
Coombes, S., Lai, Y. M., Sayli, M., & Thul, R. (in press). Networks of piecewise linear neural mass models. European Journal of Applied Mathematics, doi:10.1017/S0956792518000050. ISSN 0956-7925

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

The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions (2017)
Journal Article
Gökçe, A., Avitabile, D., & Coombes, S. (in press). The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions. Journal of Mathematical Neuroscience, 7, doi:10.1186/s13408-017-0054-4. ISSN 2190-8567

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 unbounded domains. Neural field... Read More

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), doi:10.1186/s13408-017-0051-7. ISSN 2190-8567

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

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), doi:10.1007/s10827-017-0655-7. ISSN 0929-5313

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

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, doi:10.1016/j.physd.2017.02.017. ISSN 0167-2789

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

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. doi: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

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, doi:10.1007/978-3-319-44778-0_48. ISSN 0302-9743

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

Synchrony in networks of coupled non-smooth dynamical systems: extending the master stability function (2016)
Journal Article
Coombes, S., & Thul, R. (2016). Synchrony in networks of coupled non-smooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, doi:10.1017/S0956792516000115. ISSN 0956-7925

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

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, doi:10.1186/s13408-016-0035-z. ISSN 2190-8567

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

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, doi:10.1186/s13408-015-0033-6. ISSN 2190-8567

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

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

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), doi:10.1016/j.bbamcr.2015.02.019. ISSN 0167-4889

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

Spots: breathing, drifting and scattering in a neural field model (2014)
Book
Coombes, S., Schmidt, H., & Avitabile, D. (2014). Spots: breathing, drifting and scattering in a neural field model. In P. Beim Graben, S. Coombs, R. Potthast, & J. Wright (Eds.), Neural fields: theory and applicationsSpringer

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