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McIvor, Emma, Coombes, Stephen and Thul, Ruediger (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 . pp. 11-24. ISSN 1532-1991

Tewarie, Prejaas K., Hunt, Benjamin A. E., O'Neill, George C., Byrne, Aine, Aquino, Kevin, Bauer, Markus, Mullinger, Karen J., Coombes, Stephen and Brookes, Matthew J. (2018) Relationships between neuronal oscillatory amplitude and dynamic functional connectivity. Cerebral Cortex, 29 (6). pp. 2668-2681. ISSN 1460-2199

Nicks, Rachel, Chambon, Lucie and Coombes, Stephen (2018) Clusters in nonsmooth oscillator networks. Physical Review E, 97 (3). 032213. ISSN 2470-0053

Coombes, Stephen, Lai, Yi Ming, Sayli, Mustafa and Thul, Ruediger (2018) Networks of piecewise linear neural mass models. European Journal of Applied Mathematics . ISSN 1469-4425

Gökçe, Aytül, Avitabile, Daniele and Coombes, Stephen (2017) The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions. Journal of Mathematical Neuroscience, 7 . p. 12. ISSN 2190-8567

Byrne, Áine, Brookes, Matthew J. and Coombes, Stephen (2017) A mean field model for movement induced changes in the beta rhythm. Journal of Computational Neuroscience, 43 (2). pp. 143-158. ISSN 1573-6873

Bonilla-Quintana, Mayte, Wedgwood, Kyle C.A., O'Dea, Reuben D. and Coombes, Stephen (2017) An analysis of waves underlying grid cell firing in the medial enthorinal cortex. Journal of Mathematical Neuroscience, 7 (9). pp. 1-30. ISSN 2190-8567

Visser, Sid, Nicks, Rachel, Faugeras, Olivier and Coombes, Stephen (2017) Standing and travelling waves in a spherical brain model: the Nunez model revisited. Physica D: Nonlinear Phenomena, 349 . pp. 27-45. ISSN 0167-2789

Coombes, Stephen and Thul, Ruediger (2016) Synchrony in networks of coupled non-smooth dynamical systems: extending the master stability function. European Journal of Applied Mathematics, 27 (6). pp. 904-922. ISSN 1469-4425

Wojtak, Weronika, Coombes, Stephen, Bicho, Estela and Erlhagen, Wolfram (2016) Combining spatial and parametric working memory in a dynamic neural field model. Lecture Notes in Computer Science, 9886 . pp. 411-418. ISSN 0302-9743

Thul, Ruediger, Coombes, Stephen and Laing, Carlo R. (2016) Neural field models with threshold noise. Journal of Mathematical Neuroscience, 6 . 3/1-3/26. ISSN 2190-8567

Ashwin, Peter, Coombes, Stephen and Nicks, Rachel (2016) Mathematical frameworks for oscillatory network dynamics in neuroscience. Journal of Mathematical Neuroscience, 6 . 2/1-2/92. ISSN 2190-8567

Thul, Ruediger, Rietdorf, K., Bootman, Martin D. and Coombes, Stephen (2015) Unifying principles of calcium wave propagation: insights from a three-dimensional model for atrial myocytes. BBA Molecular Cell Research, 1853 (9). pp. 2131-2143. ISSN 0167-4889

Meijer, Hil G.E. and Coombes, Stephen (2014) Travelling waves in a neural field model with refractoriness. Journal of Mathematical Biology, 68 (5). pp. 1249-1268. ISSN 1432-1416

Meijer, Hil and Coombes, Stephen (2014) Travelling waves in models of neural tissue: from localised structures to periodic waves. EPJ Nonlinear Biomedical Physics, 2 (3). pp. 1-18. ISSN 2195-0008

Zachariou, Margarita, Alexander, Stephen P.H., Coombes, Stephen and Christodoulou, Chris (2013) A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition. PLoS ONE, 8 (3). e58296/1-e58296/23. ISSN 1932-6203

Lin, Kevin K., Wedgwood, Kyle C.A., Coombes, Stephen and Young, Lai-Sang (2013) Limitations of perturbative techniques in the analysis of rhythms and oscillations. Journal of Mathematical Biology, 66 (1-2). pp. 139-161. ISSN 0303-6812

Wedgwood, Kyle C.A., Lin, Kevin K., Thul, Ruediger and Coombes, Stephen (2013) Phase-amplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3 (2). ISSN 2190-8567

Coombes, Stephen, Thul, Ruediger and Wedgwood, Kyle C.A. (2012) Nonsmooth dynamics in spiking neuron models. Physica D, 241 (22). pp. 2042-2057. ISSN 0167-2789

Hlinka, Jaroslav and Coombes, Stephen (2012) Using computational models to relate structural and functional brain connectivity. European Journal of Neuroscience, 36 (2). pp. 2137-2145. ISSN 0953-816X

Svensson, Carl-Magnus, Coombes, Stephen and Peirce, Jonathan (2012) Using evolutionary algorithms for fitting high-dimensional models to neuronal data. Neuroinformatics, 10 (2). pp. 199-218. ISSN 1539-2791

Coombes, Stephen, Thul, Ruediger, Laudanski, Jonathan, Palmer, Alan and Sumner, Chris (2012) Neuronal spike-train responses in the presence of threshold noise. Frontiers in Life Science, 5 (3-4). pp. 91-105. ISSN 2155-3769

Coombes, Stephen, Schmidt, Helmut and Bojak, Ingo (2012) Interface dynamics in planar neural field models. Journal of Mathematical Neuroscience . ISSN 2190-8567 (In Press)

Thul, Ruediger, Coombes, Stephen and Bootman, Martin D. (2012) Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves. Frontiers in Physiology, 3 . p. 279. ISSN 1664-042X

Thul, Ruediger, Coombes, Stephen, Roderick, H. Llewelyn and Bootman, Martin D. (2012) Subcellular calcium dynamics in a whole-cell model of an atrial myocyte. Proceedings of the National Academy of Sciences, 109 (6). pp. 2150-2155. ISSN 1091-6490

Coombes, Stephen and Laing, Carlo (2011) Pulsating fronts in periodically modulated neural field models. Physical Review E . ISSN 1539-3755 (In Press)

Laudanski, Jonathan, Sumner, Chris and Coombes, Stephen (2010) Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map. Physical Review E, 82 (1). e011924. ISSN 1539-3755

Hlinka, Jaroslav and Coombes, Stephen (2010) Depolarization induced suppression of excitation and the emergence of ultra-slow rhythms in neural networks. Physical Review Letters . ISSN 0031-9007 (In Press)

Coombes, Stephen and Schmidt, Helmut (2010) Neural fields with sigmoidal firing rates: approximate solutions. Discrete and Continuous Dynamical Systems. Series S . ISSN 1937-1632 (Submitted)

Thul, Ruediger and Coombes, Stephen (2010) Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20 . 045102. ISSN 1054-1500

Coombes, Stephen (2009) Large-scale neural dynamics: simple and complex. NeuroImage . ISSN 1053-8119 (In Press)

Svensson, Carl-Magnus and Coombes, Stephen (2009) Mode locking in a spatially extended neuron model: active soma and compartmental tree. International Journal of Bifurcation and Chaos . ISSN 0218-1274 (In Press)

Thul, Ruediger, Coombes, Stephen and Smith, G.D. (2009) Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D, 238 . pp. 2142-2152. ISSN 0167-2789

Coombes, Stephen (2008) Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models. SIAM Journal on Applied Dynamical Systems . (In Press)

Zachariou, Margarita, Dissanayake, Dilshani W N, Coombes, Stephen, Owen, Markus R. and Mason, Robert (2008) Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis. Cognitive Neurodynamics, 2 . pp. 159-170. ISSN 1871-4099

Thul, Ruediger, Smith, G.D. and Coombes, Stephen (2008) A bidomain threshold model of propagating calcium waves. Journal of Mathematical Biology, 56 (4). pp. 435-463. ISSN 1432-1416

Coombes, Stephen and Laing, Carlo (2008) Delays in activity based neural networks. Philosophical Transactions of the Royal Society A . ISSN 1364-503X (In Press)

Owen, Markus R., Laing, Carlo and Coombes, Stephen (2007) Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9 (378). ISSN 1367-2630

Coombes, Stephen, Venkov, Nikola, Shiau, LieJune, Bojak, Ingo, Liley, David and Laing, Carlo (2007) Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76 . 051901-051908. (Submitted)

Venkov, Nikola Atanasov, Coombes, Stephen and Matthews, Paul C (2007) Dynamic instabilities in scalar neural field equations with space-dependent delays.

Coombes, Stephen, Timofeeva, Yulia, Svennson, Carl-Magnus, Lord, Gabriel, Josic, Kresimir, Cox, Steven J. and Colbert, Costa (2007) Branching dendrites with resonant membrane: a "sum-over-trips" approach. Biological Cybernetics, 97 (2). pp. 137-149. ISSN 0340-1200

Coombes, Stephen and Owen, Markus R. (2007) Exotic dynamics in a firing rate model of neural tissue with threshold accommodation.

Zachariou, Margarita, Dissanayake, Dilshani, Owen, Markus R., Mason, Rob and Coombes, Stephen (2006) The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study. Neurocomputing, 70 (10/12). pp. 1902-1906. ISSN 0925-2312

Coombes, Stephen, Doiron, Brent, Josic, Kresimir and Shea-Brown, Eric (2006) Toward blueprints for network architecture, biophysical dynamics, and signal transduction.

Chow, Carson and Coombes, Stephen (2006) Existence and wandering of bumps in a spiking neural network model.

Timofeeva, Yulia, Lord, Gabriel and Coombes, Stephen (2006) Spatio-temporal filtering properties of a dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework. (Unpublished)

Laing, Carlo and Coombes, Stephen (2005) The importance of different timings of excitatory and inhibitory pathways in neural field models.

Timofeeva, Yulia, Lord, Gabriel and Coombes, Stephen (2005) Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework.

Coombes, Stephen and Owen, Markus R. (2005) Bumps, breathers, and waves in a neural network with spike frequency adaptation. Physical Review Letters, 94 (14). pp. 148102-1. ISSN 1079-7114

Coombes, Stephen (2005) Waves, bumps, and patterns in neural field theories.

Timofeeva, Yulia and Coombes, Stephen (2004) Directed percolation in a two dimensional stochastic fire-diffuse-fire model.

Coombes, Stephen and Owen, Markus R. (2004) Evans functions for integral neural field equations with Heaviside firing rate function. SIAM Journal on Applied Dynamical Systems, 3 (4). pp. 574-600. ISSN 1536-0040

Chik, D T W, Coombes, Stephen and Wang, Z D (2004) Clustering through post inhibitory rebound in synaptically coupled neurons.

Laing, Carlo and Coombes, Stephen (2004) Mode locking in a periodically forced "ghostbursting" neuron model.

Coombes, Stephen, Hinch, Robert and Timofeeva, Yulia (2004) Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release.

Timofeeva, Yulia, Cox, Steven J., Coombes, Stephen and Josic, Kresimir Democratization in a passive dendritic tree: an analytical investigation. Journal of Computational Neuroscience . ISSN 0929-5313 (In Press)

Laing, Carlo and Coombes, Stephen Instabilities in threshold-diffusion equations with delay. Physica D . ISSN 0167-2789 (In Press)

Book Section

Coombes, Stephen (2015) Mathematical neuroscience: from neurons to networks. In: Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques, Caen, pp. 153-160. ISBN 9782954122137

Coombes, Stephen, Schmidt, Helmut and Avitabile, Daniele (2014) Spots: breathing, drifting and scattering in a neural field model. In: Neural fields: theory and applications. Springer, Berlin, pp. 187-211. ISBN 9783642545931

Thul, Ruediger, Bellamy, Tom, Roderick, Llewelyn, Bootman, Martin and Coombes, Stephen (2007) Calcium oscillations. In: Cellular Oscillatory Mechanisms. Advances in experimental medicine and biology (641). Springer, New York, pp. 1-27. ISBN 9780387097930

Coombes, Stephen and Zachariou, Margarita Gap junctions and emergent rhythms. In: Coherent Behavior in Neuronal Networks. Springer. (Submitted)