Stephen Coombes Professor of Applied Mathematics
Google Scholar Citations ORCID ResearcherID MathSciNet

Editorial and advisory boards

Journal of Mathematical Neuroscience Physica D Bulletin of Mathematical Biology Mathematical Neuroscience and Applications Journal of Computational Neuroscience

Preprints & submitted work

  1. J Ross, B Skelly, Z Seedat, M Brookes, S Coombes, and Á Byrne 2026 A stochastic neural mass model for cortical beta bursts in Parkinson's disease, submitted
  2. S Coombes, R Thul, S Ruschel, and R Nicks 2026 A rate–timing reduction for event-based spiking neural networks, in prep
  3. G Jolly, R Nicks, S Ruschel, G Iskenderoglu, and S Coombes 2026, Phase oscillator networks with multiple and state-dependent delays: A framework for exploring white matter plasticity in neurodynamics, submitted
  4. S Ruschel, E Hristov, H G E Meijer, S Coombes, and R Nicks 2026 Network attractors driven by time-delay plasticity, submitted
  5. S Coombes and H G E Meijer 2026 Synchrony in firing rate neural networks with multiple delays: A harmonic balance approach, Mathematical Neuroscience and its Applications, under revision

Published work

  1. S Coombes, R Thul, S Ruschel, and R Nicks 2026 Adaptive conduction delays and phase locking in spiking Haken Lighthouse networks, Biological Cybernetics, Vol 120:37
  2. O Cattell, R D O’Dea, and S Coombes 2026 Travelling fronts in a generalised neural field model that couples to the extracellular space, Physical Review E, Vol 114, 024409
  3. O Cattell, A Mayora-Cebollero, R D O’Dea, R Barrio, and S Coombes 2026 Understanding tonic-clonic seizure transitions as secondary bifurcations in a neural field model, Proceedings of the Royal Society A, Vol 482 (2338): 20250452
  1. S Coombes 2025 Revisiting the Haken Lighthouse Model, The European Physical Journal Special Topics: In Memoriam Hermann Haken: Synergetics and Self-organisation in Complex Systems
  2. C Scholes, S Coombes, A R Palmer, W S Rhode, R Mill and C J Sumner 2025 Precise spike-timing information in the brainstem is well aligned with the needs of communication and the perception of environmental sounds, PLoS Biology, 23(6): e3003213
  1. M Forrester, S Petros, O Cattell, Y-M Lai, R D O'Dea, S Sotiropoulos and S Coombes 2024 Whole brain functional connectivity: insights from next generation neural mass modelling incorporating electrical synapses, PLoS Computational Biology, Vol 20, e1012647
  2. R Nicks, R Allen and S Coombes 2024 Phase and amplitude responses for delay equations using harmonic balance, Physical Review E, Vol 110, L012202
  3. S Coombes, R D O'Dea and R Nicks 2024 Brain anatomy and dynamics: A commentary on “Does the brain behave like a (complex) network? I. Dynamics” by Papo and Buldú (2024), Physics of Life Reviews, Vol 49, 38-39
  4. O Smith, S Coombes and R D O'Dea 2024 Stability analysis of electrical microgrids and their control systems, PRX Energy, Vol 3, 013011
  5. R Nicks, R Allen and S Coombes 2024 Insights into oscillator network dynamics using a phase-isostable framework, Chaos, Vol 34, 013141
  6. M Sayli and S Coombes 2024 Understanding the effect of white matter delays on large scale brain synchrony, Communications in Nonlinear Science and Numerical Simulation, Vol 131, 107803
  7. S Coombes, M Sayli, R Thul, R Nicks, M A Porter and Y M Lai 2024 Oscillatory networks: Insights from piecewise-linear modelling, SIAM Review, Vol 66, 619-679
  8. W Wojtak, S Coombes, D Avitabile, E Bicho and Wolfram Erlhagen 2024 Robust working memory in a two-dimensional continuous attractor network, Cognitive Neurodynamics, Vol 18, 3273–3289
  1. S Coombes 2023 Next generation neural population models, Frontiers in Applied Mathematics and Statistics, Vol 9
  2. S Coombes and K C A Wedgwood 2023 Neurodynamics: An Applied Mathematics Perspective, Springer (Texts in Applied Mathematics, 75)
  3. M Sayli, A C Skeldon, R Thul, R Nicks and S Coombes 2023 The two process model for sleep-wake regulation: A nonsmooth dynamics perspective, Physica D, Vol 444, 133595
  1. J Crofts, M Forrester, S Coombes and R O'Dea 2022 Structure-Function Clustering in Weighted Brain Networks, Scientific Reports, Vol 12, 16793
  2. Á Byrne, J Ross, R Nicks and S Coombes 2022 Mean-field models for EEG/MEG: from oscillations to waves, Brain Topography, Vol 35, 36-53
  1. W Wojtak, S Coombes, D Avitabile, E Bicho and W Erlhagen 2021 A dynamic neural field model of continuous input integration, Biological Cybernetics, Vol 115, 451–471
  2. R Nicks, A Cocks, D Avitabile, A Johnston and S Coombes 2021 Understanding sensory induced hallucinations: From neural fields to amplitude equations, SIAM Journal on Applied Dynamical Systems, Vol 20, 1683-1714
  3. S Modhara, Y-M Lai, R Thul and S Coombes 2021 Neural fields With rebound currents: Novel routes to patterning, SIAM Journal on Applied Dynamical Systems, Vol 20, 1596–1620
  4. P Tewarie, B Prasse, J Meier, A Byrne, M Domenico, C Stam, M Brookes, A Hillebrand, A Daffertshofer, S Coombes, P Van Mieghem 2021 Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models, New Journal of Physics, Vol 23, 063065
  5. C Tessereau, R D O’Dea, S Coombes and T Bast 2021 Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation, Brain and Neuroscience Advances, Vol 5, 1-18
  1. D Avitabile, S Coombes and P M Lima 2020 Numerical investigation of a neural field model including dendritic processing, Journal of Computational Dynamics, Vol 7, 271-290
  2. R Barrio, S Coombes, M Desroches, F Fenton, S Luther and E Pueyoh (Eds.) 2020 Excitable dynamics in neural and cardiac systems, Communications in Nonlinear Science and Numerical Simulation, Vol 86, 105275
  3. A Gökçe, D Avitabile and S Coombes 2020 Labyrinths: exotic patterns of cortical activity, The Art of Theoretical Biology, Ed. F Matthäus, S Matthäus, S Harris and T Hillen, Springer
  4. A Gökçe, S Coombes and D Avitabile 2020 Quasicrystal patterns in a neural field model, Physical Review Research, Vol 2, 013234
  5. J Ross, M Margetts, R Nicks, I Bojak, D Avitabile and S Coombes 2020 A brain-wave equation incorporating axo-dendritic connectivity, Physical Review E, Vol 101, 022411
  6. M Forrester, S Coombes, J J Crofts, S N Sotiropoulos and R D O’Dea 2020 The role of node dynamics in shaping emergent functional connectivity patterns in the brain, Network Neuroscience, 4:2, 467-483
  7. Y-Mi Lai, S Coombes and R Thul 2020 Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans, Communications in Nonlinear Science and Numerical Simulation, Vol 85, 105181
  8. Á Byrne, R O’ Dea, M Forrester, J Ross and S Coombes 2020 Next generation neural mass and field modelling, Journal of Neurophysiology, Vol 123, 726–742
  1. Y-Mi Lai, J Veasy, S Coombes and R Thul 2019 A master stability function approach to cardiac alternans, Applied Network Science, Vol 4 (90), 1-16
  2. M Sayli, Y-M Lai, S Coombes and R Thul 2019 Synchrony in networks of Franklin bells, IMA Journal of Applied Mathematics, Vol 84, 1001–1021
  3. J Veasy, Y-M Lai, S Coombes and R Thul 2019 Complex patterns of subcellular cardiac alternans, Journal of Theoretical Biology, Vol 478, 102-114
  4. P Tewarie, B A E Hunt, G C O’Neill, Á Byrne, K Aquino, M Bauer, K J Mullinger, S Coombes and M J Brookes 2019 Relationships between neuronal oscillatory amplitude and dynamic functional connectivity, Cerebral Cortex, Vol 29, 2668–2681
  5. Á Byrne, D Avitabile and S Coombes 2019 A next generation neural field model: The evolution of synchrony within patterns and waves, Physical Review E, Vol 99, 012313
  6. S Coombes and Á Byrne 2019 Next generation neural mass models, Nonlinear Dynamics in Computational Neuroscience, PoliTO Springer Series, Ed. A Torcini and F Corinto, Springer, 1-16
  7. Á Byrne, S Coombes and P F Liddle 2019 A neural mass model for abnormal beta-rebound in schizophrenia, Handbook of Multi-scale Models of Brain Disorders, Ed. V Cutsuridis, Springer.
  1. R Nicks, P Chambon and S Coombes 2018 Clusters in nonsmooth oscillator networks, Physical Review E, Vol 97, 032213.
  2. P Tewarie, R Abeysuriya, Á Byrne, G C O'Neill, S N Sotiropoulos, M J Brookes and S Coombes 2018 How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes, NeuroImage, Vol 186, 211-220.
  3. Y-M Lai, R Thul and S Coombes 2018 Analysis of networks where discontinuities and nonsmooth dynamics collide: understanding synchrony, European Physical Journal Special Topics, Vol 227, 1251–1265
  4. E McIvor, S Coombes and R Thul 2018 Three-dimensional spatio-temporal modelling of store operated Ca 2+ entry: Insights into ER refilling and the spatial signature of Ca 2+ signals, Cell Calcium, Vol 73, 11–24
  1. 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, 7:12
  2. 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, Journal of Mathematical Neuroscience, 7:9
  3. 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, Vol 43, 143-158
  4. 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
  1. 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
  2. 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
  3. R Thul, S Coombes and C R Laing 2016 Neural field models with threshold noise, Journal of Mathematical Neuroscience, 6:3
  4. P Ashwin, S Coombes and R Nicks 2016 Mathematical frameworks for oscillatory network dynamics in neuroscience, Journal of Mathematical Neuroscience, 6:2
  1. 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
  2. S Coombes 2015 Mathematical Neuroscience: from neurons to networks, EDP-Normandie Proceedings of the International Conference Symposia in Applied Mathematics, 153-160
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  1. P C Bressloff and S Coombes 2013 Neural `bubble' dynamics revisited, Cognitive Computation, Vol 5(3), 281-294
  2. S Coombes and Y Timofeeva 2013 Editorial for special issue on Neurodynamics, Journal of Mathematical Neuroscience, 3:10
  3. 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
  4. 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
  5. 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.
  6. 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
  1. 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)
  2. 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
  3. 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
  4. J Hlinka and S Coombes 2012 Using computational models to relate structural and functional brain connectivity, European Journal of Neuroscience, Vol 36, 2137–2145
  5. S Coombes, H Schmidt and I Bojak 2012 Interface dynamics in planar neural field models, Journal of Mathematical Neuroscience, 2:9.
  6. 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
  7. 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
  8. 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
  9. 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
  10. S Coombes, R Thul and K C A Wedgwood 2012 Nonsmooth dynamics in spiking neuron models, Physica D, Vol 241, 2042–2057
  11. 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
  1. 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
  2. M D Bootman, R Thul, S Coombes and H L Roderick 2011 Atrial cardiomyocyte calcium signalling, Biochimica et Biophysica Acta, Vol 1813, 922-934
  3. S Coombes and C R Laing 2011 Pulsating fronts in periodically modulated neural field models, Physical Review E, Vol 83, 011912
  1. R Thul and S Coombes 2010 Understanding cardiac alternans: a piecewise linear modelling framework, Chaos, Vol 20, 045102
  2. 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
  3. S Coombes 2010 Large-scale neural dynamics: Simple and complex, NeuroImage, Vol 52, 731–739
  4. 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
  5. 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
  6. S Coombes and Y Timofeeva 2010 Mathematical neuroscience special issue: Editorial, Physica D, Vol 239, 475-476
  7. 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
  1. 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
  2. R Thul, S Coombes and G D Smith 2009 Sensitisation of waves in a bidomain fire-diffuse-fire model of intracellular Ca 2+ dynamics, Physica D, Vol 238, 2142-2152
  3. 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
  4. S Coombes and C R Laing 2009 Delays in activity based neural networks, Philosophical Transactions of the Royal Society A, Vol 367, 1117-1129
  5. S Coombes and C R Laing 2009 Instabilities in threshold-diffusion equations with delay, Physica D, Vol 238, 264-272
  1. 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
  2. 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.
  3. 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
  4. 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
  5. 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
  1. 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.
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. S Coombes 2007 Mathematical neuroscience, Journal of Mathematical Biology, Vol 54, 305-307
  1. 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
  2. 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
  3. S Coombes (2006) Neural fields . Scholarpedia, 1(6):1373
  4. P C Bressloff and S Coombes 2006 Editorial: Special issue on Neural Development, Mathematical Medicine & Biology, Vol 23, 77-78
  5. 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
  6. 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
  7. 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
  8. 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
  1. S Coombes and P C Bressloff (Editors) 2005 Bursting: The Genesis of Rhythm in the Nervous System, World Scientific Press. MathSciNet Review.
  2. S Coombes 2005 Waves, bumps, and patterns in neural field theories, Biological Cybernetics, Vol 93, 91-108.
  3. 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.
  4. 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
  1. Y Timofeeva and S Coombes 2004 Directed percolation in a two dimensional stochastic fire-diffuse-fire model, Physical Review E, Vol 70, 062901-3
  2. 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 3, 574-600
  3. 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
  4. 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
  1. 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
  2. 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
  3. 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
  4. Y Timofeeva and S Coombes 2003 A stochastic fire-diffuse-fire model of Calcium release, FORMA, Vol 18, 53-58
  5. 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
  6. 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
  7. M Denman-Johnson and S Coombes 2003 A continuum of weakly coupled McKean neurons, Physical Review E, Vol 67, 051903
  8. S Coombes 2003 Dynamics of synaptically coupled integrate-and-fire-or-burst neurons, Physical Review E, Vol 67, 041910
  9. 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
  1. 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
  1. S Coombes 2001 Phase-locking in networks of pulse-coupled McKean relaxation oscillators, Physica D, Vol 160, 173-188
  2. 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.
  3. S Coombes 2001 The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca 2+ release, Bulletin of Mathematical Biology, Vol 63, 1-20.
  4. 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
  5. S Coombes 2001 From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves, Mathematical Biosciences, 170, 155-172
  1. P C Bressloff and S Coombes 2000 Dynamics of strongly-coupled spiking neurons, Neural Computation, Vol 12, 91-129
  2. 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.
  3. 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.
  4. 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
  1. 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
  2. S Coombes 1999 Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems, Physics Letters A, Vol 255, 49-57
  3. 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
  4. 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
  5. 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
  1. 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)
  2. 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
  3. 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
  4. 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
  1. S Coombes and G J Lord 1997 Desynchronization of pulse-coupled integrate-and-fire neurons, Phys. Rev. E., Vol 55, No 3, R2104-R2107
  2. 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
  3. 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
  4. P C Bressloff and S Coombes 1997 Physics of the extended neuron, International Journal of Modern Physics B, Vol 11, No 20, 2343-2392
  5. 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
  6. 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
  1. 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
  2. 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
  3. 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
  4. 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
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  1. 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.
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