Google Scholar Citations Orcid ID ResearcherID MathSciNet

Preprints

Á Byrne, D Avitabile and S Coombes 2017 A next generation neural field model: The evolution of synchrony within patterns and waves
A Gökçe, D Avitabile and S Coombes 2017 The dynamics of neural fields on bounded domains: an interface approach for Dirichlet boundary conditions, Journal of Mathematical Neuroscience, submitted
M Bonilla-Quintana, K C A Wedgwood, R D O’Dea and S Coombes 2017 An analysis of waves underlying grid cell firing in the medial enthorinal cortex, submitted
A Gökçe, D Avitabile and S Coombes 2017 Neural fields: Localised states with piece-wise constant interactions, NeuroMath, INdAM Series, Springer, to appear
Á Byrne, M J Brookes and S Coombes 2017 A mean field model for movement induced changes in the beta rhythm, Journal of Computational Neuroscience, to appear
S Coombes and Á Byrne 2017 Next generation neural mass models, Lecture Notes in Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT, Ed. A Torcini and F Corinto, Springer

Published

S Visser, R Nicks, O Faugeras and S Coombes, 2017 Standing and travelling waves in a spherical brain model: the Nunez model revisited, Physica D, Vol 349, 27–45


W Wojtak, S Coombes, E Bicho, W Erlhagen 2016 Combining Spatial and Parametric Working Memory in a Dynamic Neural Field Model, Artificial Neural Networks and Machine Learning – ICANN 2016, Proceedings, Part I, 411–418
S Coombes and R Thul 2016 Synchrony in networks of coupled nonsmooth dynamical systems: Extending the master stability function, European Journal of Applied Mathematics, Vol 27(6), 904–922
R Thul, S Coombes and C R Laing 2016 Neural field models with threshold noise, Journal of Mathematical Neuroscience, 6:3
P Ashwin, S Coombes and R Nicks 2016 Mathematical frameworks for oscillatory network dynamics in neuroscience, Journal of Mathematical Neuroscience, 6:2


R Thul, K Rietdorf, M D Bootman and S Coombes 2015 Unifying principles of calcium wave propagation - insights from a three-dimensional model for atrial myocytes, Biochimica et Biophysica Acta Molecular Cell Research, Vol 1853(9), 2131–2143
S Coombes 2015 Mathematical Neuroscience: from neurons to networks, EDP-Normandie Proceedings of the International Conference Symposia in Applied Mathematics, 153-160


S Coombes, H Schmidt and D Avitabile 2014 Spots: Breathing, drifting and scattering in a neural field model, Neural Fields, Ed. S Coombes, P beim Graben, R Potthast and J J Wright, Springer Verlag
S Coombes, P beim Graben and R Potthast 2014 Tutorial on Neural Field Theory, Neural Fields, Ed. S Coombes, P beim Graben, R Potthast and J J Wright, Springer Verlag
H G E Meijer and S Coombes 2014 Travelling waves in models of neural tissue: from localised structures to periodic waves, EPJ Nonlinear Biomedical Physics, Vol 2:3
Y Timofeeva and S Coombes 2014 Network response of gap junction coupled dendrites, Dendritic computations through morphology and connectivity, in The Computing Dendrite: From Structure to Function, Ed. H Cuntz, M Remme, B Torben-Nielsen, Springer
H G E Meijer and S Coombes 2014 Travelling waves in a neural field model with refractoriness, Journal of Mathematical Biology, Vol 68(5), 1249-1268


P C Bressloff and S Coombes 2013 Neural `bubble' dynamics revisited, Cognitive Computation, Vol 5(3), 281-294
S Coombes and Y Timofeeva 2013 Editorial for special issue on Neurodynamics, Journal of Mathematical Neuroscience, 3:10
Y Timofeeva, S Coombes and D Michieletto 2013 Gap junctions, dendrites and resonances: a recipe for tuning network dynamics, Journal of Mathematical Neuroscience, 3:15
M Zachariou, S Alexander, S Coombes and C Christodoulou 2013 A biophysical model of endocannabinoid-mediated short term depression in hippocampal inhibition, PLoS ONE, 8(3): e58926
K C A Wedgwood, K K Lin, R Thul and S Coombes 2013 Phase-amplitude descriptions of neural oscillator models, Journal of Mathematical Neuroscience, 3:2.
K K Lin, K C A Wedgwood, S Coombes and L-S Young 2013 Limitations of perturbative techniques in the analysis of rhythms and oscillations, Journal of Mathematical Biology, Vol 66, 139-161


A Langdon, M Breakspear and S Coombes 2012 Phase locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations, Physical Review E, Vol 86, 061903(1-12)
R Thul, S Coombes and M D Bootman 2012 Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves, Frontiers in Computational Physiology and Medicine, Vol 3, 279
S Coombes and J R Terry 2012 Editorial: The Dynamics of Neurological Disease: Integrating Computational, Experimental and Clinical Neuroscience, European Journal of Neuroscience, Vol 36, 2118–2120
J Hlinka and S Coombes 2012 Using computational models to relate structural and functional brain connectivity, European Journal of Neuroscience, Vol 36, 2137–2145
S Coombes, H Schmidt and I Bojak 2012 Interface dynamics in planar neural field models, Journal of Mathematical Neuroscience, 2:9.
R Thul, S Coombes, H L Roderick and M D Bootman 2012 Subcellular calcium dynamics in a whole cell model of an atrial myocyte, Proceedings of the National Academy of Sciences, Vol 109, 2150-2155
C-M Svensson, S Coombes and J W Peirce 2012 Using evolutionary algorithms for fitting high-dimensional models to neuronal data, Neuroinformatics, Vol 10, 199-218
S Coombes, C R Laing, H Schmidt, N Svanstedt and J A Wyller 2012 Waves in random neural media, Discrete and Continuous Dynamical Systems Series A, Vol 32, 2951 - 2970
H G Rotstein, S Coombes and A-M Gheorghe 2012 Canard-like explosion of limit cycles in two-dimensional piecewise-linear models of FitzHugh-Nagumo type, SIAM Journal on Applied Dynamical Systems, Vol 11, 135-180
S Coombes, R Thul and K C A Wedgwood 2012 Nonsmooth dynamics in spiking neuron models, Physica D, Vol 241, 2042–2057
J Taxidis, S Coombes, R Mason and M R Owen 2012 Modeling sharp wave - ripple complexes through a CA3-CA1 network model with chemical synapses, Hippocampus, Vol 22, 995–1017

S Coombes, R Thul, J Laudanski, A R Palmer and C J Sumner 2011 Neuronal spike-train responses in the presence of threshold noise, Frontiers in Life Science, Vol 5, 91-105
M D Bootman, R Thul, S Coombes and H L Roderick 2011 Atrial cardiomyocyte calcium signalling, Biochimica et Biophysica Acta, Vol 1813, 922-934
S Coombes and C R Laing 2011 Pulsating fronts in periodically modulated neural field models, Physical Review E, Vol 83, 011912

R Thul and S Coombes 2010 Understanding cardiac alternans: a piecewise linear modelling framework, Chaos, Vol 20, 045102
J Laudanski, C J Sumner and S Coombes 2010 Calcium window currents, periodic forcing and chaos: Understanding single neuron response with a discontinuous one dimensional map, Physical Review E, Vol 82, 011924
S Coombes 2010 Large-scale neural dynamics: Simple and complex, NeuroImage, Vol 52, 731–739
S Coombes and H Schmidt 2010 Neural fields with sigmoidal firing rates: approximate solutions, Discrete and Continuous Dynamical Systems Series A, Vol 28, 1369 - 1379
J Laudanski, S Coombes, A R Palmer and C J Sumner 2010 Mode-locked spike trains in responses of ventral cochlear nucleus chopper and onset neurons to periodic stimuli, Journal of Neurophysiology, Vol 103, 1226-1237
S Coombes and Y Timofeeva 2010 Mathematical neuroscience special issue: Editorial, Physica D, Vol 239, 475-476
J Hlinka and S Coombes 2010 Depolarization induced suppression of excitation and the emergence of ultra-slow rhythms in neural networks, Physical Review Letters, Vol 104, 068101

C-M Svensson and S Coombes 2009 Mode locking in a spatially extended neuron model: active soma and compartmental tree, International Journal of Bifurcation and Chaos, Vol 19, 2597-2607
R Thul, S Coombes and G D Smith 2009 Sensitisation of waves in a bidomain fire-diffuse-fire model of intracellular Ca2+ dynamics, Physica D, Vol 238, 2142-2152
S Coombes and M Zachariou 2009 Gap junctions and emergent rhythms, Coherent Behavior in Neuronal Networks (Ed. Rubin, Josic, Matias, Romo), Springer, Computational Neuroscience series
S Coombes and C R Laing 2009 Delays in activity based neural networks, Philosophical Transactions of the Royal Society A, Vol 367, 1117-1129
S Coombes and C R Laing 2009 Instabilities in threshold-diffusion equations with delay, Physica D, Vol 238, 264-272

Y Timofeeva, S J Cox, S Coombes and K Josic 2008 Democratization in a passive dendritic tree: an analytical investigation, Journal of Computational Neuroscience, Vol 25, 228-244
M Zachariou, D W N Dissanayake, S Coombes, M R Owen, R Mason 2008 Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis, Cognitive Neurodynamics, Vol 2, 159-170.
S Coombes 2008 Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models, SIAM Journal on Applied Dynamical Systems, Vol 7, 1101-1129
R Thul, T C Bellamy, H L Roderick, M D Bootman and S Coombes 2008 Calcium Oscillations, Cellular Oscillatory Mechanisms (Ed. Miguel Maroto and Nick Monk), Springer, Advances in Experimental Medicine and Biology
R Thul, G D Smith and S Coombes 2008 A bidomain threshold model of propagating calcium waves, Journal of Mathematical Biology, Vol 56, 435-463

S Coombes, N A Venkov, L Shiau, I Bojak, D T J Liley and C R Laing 2007 Modeling electrocortical activity through improved local approximations of integral neural field equations, Physical Review E, Vol 76, 051901-8.
M R Owen, C R Laing and S Coombes 2007 Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities, New Journal of Physics, Vol 9, 378
S Coombes and M R Owen 2007 Exotic dynamics in a firing rate model of neural tissue with threshold accommodation, AMS Contemporary Mathematics, Vol 440 "Fluids and Waves: Recent Trends in Applied Analysis", (Ed. Fernanda Botelho, Thomas Hagen, and James Jamison), 123-144
S Coombes, Y Timofeeva, C-M Svensson, G J Lord, K Josic, S J Cox and C M Colbert 2007 Branching Dendrites with Resonant Membrane: A "sum-over-trips" approach, Biological Cybernetics, Vol 97, 137-149
N A Venkov, S Coombes and P C Matthews 2007 Dynamic instabilities in scalar neural field equations with space-dependent delays, Physica D, Vol 232, 1-15
M Zachariou, W D N Dissanayake, M R Owen, R Mason and S Coombes 2007 The Role of Cannabinoids in the Neurobiology of Sensory Gating: A firing rate model study, Neurocomputing, Vol 70, 1902-1906
S Coombes 2007 Mathematical neuroscience, Journal of Mathematical Biology, Vol 54, 305-307

S Coombes, B Doiron, K Josic and E Shea-Brown 2006 Toward blueprints for network architecture, biophysical dynamics, and signal transduction, Philosophical Transactions of the Royal Society A, Vol 364, 3301-3318
M D Bootman, D R Higazi, S Coombes and H L Roderick 2006 Calcium signalling during excitation-contraction coupling in mammalian atrial myocytes, Journal of Cell Science, Vol 119, 3915-3925
S Coombes (2006) Neural fields. Scholarpedia, 1(6):1373
P C Bressloff and S Coombes 2006 Editorial: Special issue on Neural Development, Mathematical Medicine & Biology, Vol 23, 77-78
C C Chow and S Coombes 2006 Existence and wandering of bumps in a spiking neural network model, SIAM Journal on Applied Dynamical Systems, Vol 5, 552-574
Y Timofeeva, G J Lord and S Coombes 2006 Spatio-temporal filtering properties of a dendritic cable with active spines, Journal of Computational Neuroscience, Vol 21, 293-306
C R Laing and S Coombes 2006 The importance of different timings of excitatory and inhibitory pathways in neural field models, Network, Vol 17, 151-172
Y Timofeeva, G J Lord and S Coombes 2006 Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework, Neurocomputing,Vol 69, 1058-1061

S Coombes and P C Bressloff (Editors) 2005 Bursting: The Genesis of Rhythm in the Nervous System, World Scientific Press. MathSciNet Review.
S Coombes 2005 Waves, bumps, and patterns in neural field theories, Biological Cybernetics, Vol 93, 91-108.
S Coombes and M R Owen 2005 Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters, Vol 94, 148102.
C R Laing and S Coombes 2005 Mode-locking in a periodically forced "ghostbursting" neuron model, International Journal of Bifurcation and Chaos, Vol 15, 1433-1444

Y Timofeeva and S Coombes 2004 Directed percolation in a two dimensional stochastic fire-diffuse-fire model, Physical Review E, Vol 70, 062901-3
S Coombes and M R Owen 2004 Evans functions for integral neural field equations with Heaviside firing rate function SIAM Journal on Applied Dynamical Systems, Vol 34, 574-600
D T W Chik, S Coombes and Z D Wang 2004 Clustering through post inhibitory rebound in synaptically coupled neurons, Physical Review E, Vol 70, 011908
S Coombes, R Hinch and Y Timofeeva 2004 Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release, Progress in Biophysics and Molecular Biology, Vol 85, 197-216

Y Timofeeva and S Coombes 2003 Wave bifurcation and propagation failure in a model of Calcium release, Journal of Mathematical Biology, Vol 47, 249-269
S Coombes and Y Timofeeva 2003 Sparks and waves in a stochastic fire-diffuse-fire model of Calcium release, Physical Review E, Vol 68, 021915
S Coombes and P C Bressloff 2003 Saltatory waves in the spike-diffuse-spike model of active dendritic spines, Physical Review Letters, Vol 91, 028102
Y Timofeeva and S Coombes 2003 A stochastic fire-diffuse-fire model of Calcium release, FORMA, Vol 18, 53-58
S Coombes G J Lord and M R Owen 2003 Waves and bumps in neuronal networks with axo-dendritic synaptic interactions, Physica D, Vol 178, 219-241
M P James, S Coombes and P C Bressloff 2003 The effects of quasi-active membrane on multiply periodic traveling waves in integrate-and-fire systems, Physical Review E, Vol 67, 051905
M Denman-Johnson and S Coombes 2003 A continuum of weakly coupled McKean neurons, Physical Review E, Vol 67, 051903
S Coombes 2003 Dynamics of synaptically coupled integrate-and-fire-or-burst neurons, Physical Review E, Vol 67, 041910
P C Bressloff and S Coombes 2003 Synchronization of synaptically-coupled neural oscillators. In: Epilepsy as a dynamic disease (Springer-Verlag), J Milton and P Jung editors, chapter 7

G J Lord and S Coombes 2002 Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue, Physica D, Vol 161, 1-20

S Coombes 2001 Phase-locking in networks of pulse-coupled McKean relaxation oscillators, Physica D, Vol 2820, 1-16
S Coombes, M R Owen and G D Smith 2001 Mode-locking in a periodically forced integrate-and-fire-or-burst neuron model, Physical Review E, 64, 041914.
S Coombes 2001 The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca2+ release, Bulletin of Mathematical Biology, Vol 63, 1-20.
P C Bressloff and S Coombes 2001 Mathematical reduction techniques for modelling biophysical neural networks, Biophysical Neural Networks, Ed. Roman R Poznanski, Gordon and Breach Scientific Publishers
S Coombes 2001 From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves, Mathematical Biosciences, 170, 155-172

P C Bressloff and S Coombes 2000 Dynamics of strongly-coupled spiking neurons, Neural Computation, Vol 12, 91-129
S Coombes and P C Bressloff 2000 Solitary waves in a model of dendritic cable with active spines, SIAM J Appl Math, Vol 61, 432-453.
P C Bressloff and S Coombes 2000 A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators, SIAM J Appl Math, Vol 60, 820-841.
S Coombes and A H Osbaldestin 2000 Period adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator, Physical Review E, Vol 62, 4057-4066

P C Bressloff and S Coombes 1999 Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays, Physica D, Vol 130, 232-254
S Coombes 1999 Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems, Physics Letters A, Vol 255, 49-57
S Coombes and P C Bressloff 1999 Mode-locking and Arnold tongues in integrate-and-fire neural oscillators, Physical Review E, Vol 60, 2086-2096
S Coombes 1999 Chaos in integrate-and-fire dynamical systems, Proceedings of Stochastic and Chaotic Dynamics in the Lakes, American Institute of Physics Conference Proceedings, 502, 88-93
M P James, P C Bressloff and S Coombes 1999, Adapting Synapses in Pulse-Coupled Oscillators, Proceedings of Stochastic and Chaotic Dynamics in the Lakes, American Institute of Physics Conference Proceedings, 502, 112-117

P C Bressloff and S Coombes 1998 Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays, Physica D, 126, 99-122 (1999)
P C Bressloff and S Coombes 1998 Travelling waves in a chain of pulse-coupled oscillators, Physical Review Letters, Vol.80, No.21, 4815-4818
P C Bressloff and S Coombes 1998 Desynchronization, mode locking, and bursting in strongly coupled integrate-and-fire oscillators, Physical Review Letters, 81, 2168-2171
P C Bressloff and S Coombes 1998 Spike train dynamics underlying pattern formation in integrate-and-fire oscillator networks, Physical Review Letters, 81, 2384-2387

S Coombes and G J Lord 1997 Desynchronization of pulse-coupled integrate-and-fire neurons, Phys. Rev. E., Vol 55, No 3, R2104-R2107
S Coombes and G J Lord 1997 Intrinsic modulation of pulse-coupled integrate-and-fire neurons, Phys. Rev. E., Vol 56, No 5, 5809-5818
P C Bressloff and S Coombes 1997 Synchrony in an array of integrate-and-fire neurons with dendritic structure, Phys. Rev. Lett, Vol 78, 4665-4668
P C Bressloff and S Coombes 1997 Physics of the extended neuron, International Journal of Modern Physics B, Vol 11, No 20, 2343-2392
P C Bressloff and S Coombes 1997 Travelling waves in a circular array of integrate-and-fire neurons, Applied Nonlinear Dynamics and Stochastic Systems Near the Millenium, eds J B Kadtke and A Bulsara, American Institute of Physics, 287-292
P C Bressloff, S Coombes and B de Souza 1997 Dynamics of a ring of pulse-coupled oscillators: group theoretic approach, Phys. Rev. Lett., Vol 79, No 15, 2791-2794

S Coombes and J G Taylor 1996 Using features for the storage of patterns in a fully connected net, Neural Networks, Vol 9, No 5, 837-844
S Coombes, S H Doole and C Campbell 1996 Central Pattern Generation in a Model Neuronal Network with Post Inhibitory Rebound and Reciprocal Inhibition, Neural Network World, Vol 6, No 2, 155-162
S Coombes and S H Doole 1996 Neuronal population dynamics with post inhibitory rebound: A reduction to piecewise linear discontinuous circle maps, Dynamics and Stability of Systems, vol 11, No 3, 193-217
S Coombes and S H Doole 1996 Neuronal populations with reciprocal inhibition and rebound currents: effects of synaptic and threshold noise, Phy. Rev. E, Vol 54, No 4, 4054-4065

S Coombes and J G Taylor 1995 The storage and stabilisation of patterns in a Hopfield net, Neural Network World, Vol 5, 2, 133-150.
I C G Campbell, S Coombes and A Surkan 1995 A constructive algorithm for building a feed-forward neural network, in Neural Networks: Artificial Intelligence and Industrial Applications, eds B. Kappen and S. Gielen (Springer-Verlag) p. 199-202.
S Coombes and J G Taylor 1995 Principal components and pattern storage in a fully connected net, Proceedings of the World Congress on Neural Networks, Washington DC, INNS Press, Vol I, 429-432.
I C G Campbell and S Coombes 1995 Optimal architectures for a class of constructive learning algorithm, Proceedings of the World Congress on Neural Networks, Washington DC, INNS Press, Vol I, 606-609.

S Coombes and J G Taylor 1994 An efficient method of pattern storage in the Hopfield net, Proceedings of the International Conference on Artificial Neural Networks, Italy, Vol 1, 443-446.

J G Taylor and S Coombes 1993 Learning higher order correlations, Neural Networks, 6, 423-428.
S Coombes and J G Taylor 1993 Using generalized principal component analysis to achieve associative memory in a Hopfield net, Network, 5, 75-88.