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Professor Stephen Coombes

Professor of Applied Mathematics, Head of Section Applied Mathematics, Faculty of Science

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Research Summary

Throughout my research career I have been working in Mathematical Neuroscience with a particular interest in the use of nonlinear dynamics to understand aspects of the human central nervous system.… read more

Selected Publications

  • BYRNE, AINE, AVITABILE, DANIELE and COOMBES, STEPHEN, 2019. PHYSICAL REVIEW E. 99(1),
  • COOMBES, STEPHEN and BYRNE, AINE, 2019. NONLINEAR DYNAMICS IN COMPUTATIONAL NEUROSCIENCE. 1-16
  • S COOMBES, Y-M LAI, M SAYLI and R THUL, 2018. Euro. Jnl of Applied Mathematics. 22
  • VISSER, S., NICKS, R., FAUGERAS, O. and COOMBES, S., 2017. PHYSICA D-NONLINEAR PHENOMENA. 349, 27-45
  • Nottingham is host to the
  • I am co-editor in chief of the

Current Research

Throughout my research career I have been working in Mathematical Neuroscience with a particular interest in the use of nonlinear dynamics to understand aspects of the human central nervous system. These long-term goals have required me to build up, and help develop, a wide-ranging set of mathematical tools (for describing single cells through to networks). This has led to the development of Evans function techniques for the analysis of wave stability in neural fields as well as pioneered the use of nonsmooth dynamics for understanding spiking network states. In parallel with these theoretical developments, I have set out on the journey to learn the language of the experimentalists and now work in an environment that allows extensive collaboration with experimental groups within the 糖心原创, including the Sir Peter Mansfield Imaging Centre, the MRC Institute of hearing research, Psychology, Electrophysiology, and the Nottingham Beacon in Precision Imaging. Such interaction has showcased the important contributions that mathematics can make to neuroscience. I am actively championing this new field of mathematics at the national and international level, co-ordinating a and co-creating the new .

I have made substantial contributions to neural field models of cortical and thalamic neural tissue. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around extensions of those used for local differential equation models. I am actively working to develop the mathematics relevant to heterogeneity, noise, delays, and plasticity in neural systems, and provide a focal point for community activity by organising conferences in these areas, most recently in France 2015 and 2016 (as co-founder of the International Conference on Mathematical Neuroscience series). My current mathematical work impacts on the analysis of brain rhythms seen in electro- and magneto-encephalography recordings, mode-locked spike trains seen in auditory neurons, models of branched dendritic tissue with active spines, neural network models of fear memory, and models of reinforcement learning in neural field models for spatial navigation.

Future Research

I am developing new dynamical models of neural tissue with connectome data describing the anatomical structure of individual brains, to gain a perspective on whole brain dynamics. A current use of the model is for in-silico experiments to help improve the design of transcranial magnetic stimulation protocols for the treatment of mental health conditions.

  • COOMBES, STEPHEN and BYRNE, AINE, 2019. NONLINEAR DYNAMICS IN COMPUTATIONAL NEUROSCIENCE. 1-16
  • VEASY, JOSHUA, LAI, YI MING, COOMBES, STEPHEN and THUL, RUDIGER, 2019. JOURNAL OF THEORETICAL BIOLOGY. 478, 102-114
  • BYRNE, AINE, AVITABILE, DANIELE and COOMBES, STEPHEN, 2019. PHYSICAL REVIEW E. 99(1),
  • S COOMBES, Y-M LAI, M SAYLI and R THUL, 2018. Euro. Jnl of Applied Mathematics. 22
  • 脕 BYRNE, S COOMBES and P LIDDLE, 2018. A neural mass model for abnormal beta-rebound in schizophrenia. In: Handbook of Multi-scale Models of Brain Disorders Springer.. (In Press.)
  • A G脰K脟E, D AVITABILE and S COOMBES, 2018. Neural fields: Localised states with piece-wise constant interactions In: NeuroMath, INdAM Series, Springer. (In Press.)
  • R NICKS, L CHAMBON and S COOMBES, 2018. Physical Review E. 97, 032213
  • TEWARIE, PREJAAS, 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 (New York, N.Y. : 1991).
  • MCIVOR, EMMA, COOMBES, STEPHEN and THUL, RUDIGER, 2018. CELL CALCIUM. 73, 11-24
  • TEWARIE P, ABEYSURIYA R, BYRNE 脕, O'NEILL GC, SOTIROPOULOS SN, BROOKES MJ and COOMBES S, 2018. NeuroImage. 186, 211-220 (In Press.)
  • LAI, YI MING, THUL, RUDIGER and COOMBES, STEPHEN, 2018. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS. 227(10-11), 1251-1265
  • BYRNE, AINE, BROOKES, MATTHEW J and COOMBES, STEPHEN, 2017. Journal of computational neuroscience.
  • VISSER, S., NICKS, R., FAUGERAS, O. and COOMBES, S., 2017. PHYSICA D-NONLINEAR PHENOMENA. 349, 27-45
  • A GOKCE, D AVITABILE and S COOMBES, 2017. Journal of Mathematical Neuroscience. (In Press.)
  • M BONILLA-QUINTANA, K C A WEDGWOOD, R O'DEA and S COOMBES, 2017. Journal of Mathematical Neuroscience. 7(9),
  • ASHWIN, PETER, COOMBES, STEPHEN and NICKS, RACHEL, 2016. Journal of mathematical neuroscience. 6(1), 2
  • S COOMBES and 脕 BYRNE, 2016. . In: Lecture Notes in Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT Springer. (In Press.)
  • S COOMBES and R THUL, 2016. European Journal of Applied Mathematics. (In Press.)
  • R THUL, S COOMBES and C R LAING, 2016. Journal of Mathematical Neuroscience. 6(3),
  • WOJTAK, WERONIKA, COOMBES, STEPHEN, BICHO, ESTELA and ERLHAGEN, WOLFRAM, 2016. ARTIFICIAL NEURAL NETWORKS AND MACHINE LEARNING - ICANN 2016, PT I. 9886, 411-418
  • THUL R, RIETDORF K, BOOTMAN MD and COOMBES S, 2015. Biochimica et biophysica acta. (In Press.)
  • S COOMBES, 2015. Mathematical Neuroscience: from neurons to networks In: EDP-Normandie Proceedings of the International Conference Symposia in Applied Mathematics.
  • COOMBES, STEPHEN, 2015. Validating Neuro-Computational Models of Neurological and Psychiatric Disorders Foreword VALIDATING NEURO-COMPUTATIONAL MODELS OF NEUROLOGICAL AND PSYCHIATRIC DISORDERS. 14, V-V
  • MEIJER HGE and COOMBES S, 2014. Journal of mathematical biology. 68(5), 1249-1268,
  • Y TIMOFEEVA and S COOMBES, 2014. . In: H CUNTZ, M REMME and B TORBEN-NIELSEN, eds., The Computing Dendrite: From Structure to Function Springer. 449-464
  • H G E MEIJER and S COOMBES, 2014. EPJ Nonlinear Biomedical Physics. 2(3),
  • S COOMBES, P BEIM GRABEN and R POTTHAST, 2014. . In: S COOMBES, P BEIM GRABEN and R POTTHAST, eds., Neural Fields: Theory and Applications Springer. 1-43
  • S COOMBES, H SCHMIDT and D AVITABILE, 2014. . In: S COOMBES, P BEIM GRABEN, R POTTHAST and J J WRIGHT, eds., Neural Fields: Theory and Applications Springer. 187-211
  • LIN KK, WEDGWOOD KCA, COOMBES S and YOUNG L, 2013. Journal of mathematical biology. 66, 139-161
  • ZACHARIOU, M., ALEXANDER, S.P.H., COOMBES, S. and CHRISTODOULOU, C., 2013. PLoS One. 8(3), e58926
  • WEDGWOOD KC, LIN KK, THUL R and COOMBES S, 2013. Journal of Mathematical Neuroscience. 3(2),
  • TIMOFEEVA Y, COOMBES S and MICHIELETTO D, 2013. Journal of mathematical neuroscience. 3(1), 15 (In Press.)
  • COOMBES S and TIMOFEEVA Y, 2013. Journal of mathematical neuroscience. 3(1), 10 (In Press.)
  • P C BRESSLOFF and S COOMBES, 2013. Cognitive Computation. 5(3), 281-294
  • ZACHARIOU M, ALEXANDER SPH, COOMBES S and CHRISTODOULOU C, 2013. PloS one. 8(3), e58926
  • TAXIDIS, J., COOMBES, S., MASON, R. and OWEN, M.R., 2012. Hippocampus. 22(5), 995-1017
  • HORACIO G. ROTSTEIN, STEPHEN COOMBES and ANA MARIA GHEORGHE, 2012. SIAM J. on Applied Dynamical Systems. 11(1), 135-180
  • THUL, R., COOMBES, S., RODERICK, H.L. and BOOTMAN, M.D., 2012. Proceedings of the National Academy of Sciences of the United States of America. 109(6), 2150-2155
  • SVENSSON, C., COOMBES, S. and PEIRCE, J.W., 2012. Neuroinformatics. 10(2), 199-218
  • COOMBES, S., THUL, R. and WEDGWOOD, K.C.A., 2012. Physica D: Nonlinear Phenomena. 241(122), 2042-2057
  • S COOMBES, C R LAING, H SCHMIDT, N SVANSTEDT and J A WYLLER, 2012. Discrete and Continuous Dynamical Systems - Series A. 32, 2951 - 2970
  • COOMBES, S., SCHMIDT, H. and BOJAK, I., 2012. Journal of Mathematical Neuroscience. 2(1), 9
  • HLINKA J and COOMBES S, 2012. The european journal of neuroscience. 36(2), 2137-45
  • COOMBES S and TERRY JR, 2012. The european journal of neuroscience. 36(2), 2118-20
  • R THUL, S COOMBES and M D BOOTMAN, 2012. Frontiers in Computational Physiology and Medicine. 3, 279
  • LANGDON, ANGELA J., BREAKSPEAR, MICHAEL and COOMBES, STEPHEN, 2012. PHYSICAL REVIEW E. 86(5), 061903(1-12)
  • BOOTMAN, MARTIN D, SMYRNIAS, IOANNIS, THUL, R脺DIGER, COOMBES, STEPHEN and RODERICK, H LLEWELYN, 2011. Biochimica et Biophysica Acta. 1813, 922-934
  • COOMBES, S. and LAING, C.R., 2011. Physical review E: Statistical, Nonlinear, and Soft Matter Physics. 83(1), 011912
  • S COOMBES, R THUL, J LAUDANSKI, A R PALMER and C J SUMNER, 2011. Frontiers in Life Science. 5, 91-105
  • COOMBES, S., 2010. NeuroImage. 52, 731-739
  • LAUDANSKI, J., COOMBES, S., PALMER, A. R. and SUMNER, C. J., 2010. Journal of Neurophysiology. 103, 1226-1237
  • COOMBES, S. and TIMOFEEVA, Y., 2010. Physica D - Nonlinear Phenomena. 239(9), 475-578
  • HLINKA, J. and COOMBES, S., 2010. Physical Review Letters. 104(6), 068101
  • COOMBES, S. and SCHMIDT, H., 2010. Discrete and Continuous Dynamical Systems Series A. 28(4), 1369-1379
  • LAUDANSKI, J., SUMNER, C. J. and COOMBES, S., 2010. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 82, 011924
  • THUL, R. and COOMBES, S., 2010. Chaos. 20(4), 045102
  • COOMBES, S. and ZACHARIOU, M., 2009. . In: JOSIC, K., RUBIN, J, MATIAS, M. and ROMO, R., eds., Coherent Behavior in Neuronal Networks Springer.
  • COOMBES, S. and LAING, C.R., 2009. Physica D: Nonlinear Phenomena. 238(3), 264-272
  • COOMBES, S. and LAING, C.R., 2009. Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences. 367(1891), 1117-1129
  • SVENSSON, C-M, and COOMBES, S., 2009. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 19(8), 2597-2607
  • ZACHARIOU, M., DISSANAYAKE, D. W., COOMBES, S., OWEN, M. R. and MASON, R., 2008. COGNITIVE NEURODYNAMICS. VOL 2(NUMBER 2), 159-170
  • THUL, R, BELLAMY, T.C., RODERICK, H.L., BOOTMAN, M.D. and COOMBES, S, 2008. . In: MIGUEL MAROTO AND NICK MONK, ed., Cellular Oscillatory Mechanisms Springer.
  • THUL, R., SMITH, G.D. and COOMBES, S., 2008. Journal of Mathematical Biology. 56(4), 435-463
  • COOMBES, S., 2008. SIAM Journal on Applied Dynamical Systems. 7(3), 1101-1129
  • TIMOFEEVA, Y., COOMBES, S., COX, S.J. and JOSIC, K., 2008. Journal of Computational Neuroscience. 25, 228-244
  • ZACHARIOU, M., DISSANAYAKE, D.W.N., OWEN, M.R., MASON, R. and COOMBES, S, 2007. Neurocomputing. 70(10-12), 1902-1906
  • BUTT, I.A. and WATTIS, J.A.D., 2007. Physica D - Nonlinear Phenomena. 231(2), 165-179
  • COOMBES, S, and OWEN, M.R., 2007. . In: BOTELHO, F., HAGEN, T. and JAMISON, J., eds., Fluids and Waves: Recent Trends in Applied Analysis 440. American Mathematical Society. 123-144
  • OWEN, M.R., LAING, C.R. and COOMBES, S., 2007. New Journal of Physics. 9, 378
  • S COOMBES, 2007. Journal of Mathematical Biology. 54(2), 305-307
  • COOMBES, S, VENKOV, N A, SHIAU, L, BOJAK, I, LILEY, D T J and LAING, C R, 2007. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 76(5 Pt 1), 051901
  • COOMBES, S., TIMOFEEVA, Y., SVENSSON, C-M., LORD, G.J., JOSIC, K., COX, S.J. and COLBERT, C.M., 2007. Biological Cybernetics. 97(2), 137-149
  • COOMBES, S., DOIRON, B., JOSI膯, K. and SHEA-BROWN, E., 2006. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical, and Engineering Sciences. 364(1849), 3301-18
  • TIMOFEEVA, Y., LORD, G. J. and COOMBES, S., 2006. Neurocomputing. VOL 69(NUMBER 10-12), 1058-1061
  • LAING, CARLO and COOMBES, STEPHEN, 2006. Network (Bristol, England). 17(2), 151-72
  • S COOMBES, 2006. Available at: <http://www.scholarpedia.org/article/Neural_Fields>
  • TIMOFEEVA, YULIA, LORD, GABRIEL J and COOMBES, STEPHEN, 2006. Journal of computational neuroscience.. 21(3), 293-306
  • CHOW, C. C. and COOMBES, S., 2006. SIAM Journal on Applied Dynamical Systems. 5(4), 552-574
  • P C BRESSLOFF AND S COOMBES, 2006. Mathematical Medicine & Biology. 23(2), 77-78
  • BOOTMAN, MARTIN D, HIGAZI, DANIEL R, COOMBES, STEPHEN and RODERICK, H LLEWELYN, 2006. Journal of Cell Science. 119(Pt 19), 3915-25
  • COOMBES, S. and OWEN, M.R., 2005. Physical Review Letters. VOL 94(NUMB 14), 148102
  • COOMBES,S. and BRESSLOFF,P.C., eds., 2005. Singapore; World Scientific Publishing.
  • COOMBES, S., 2005. Biological Cybernetics. VOL 93(NUMBER 2), 91-108
  • LAING, C. R. and COOMBES, S., 2005. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. VOL 15(NUMB 4), 1433-1444
  • COOMBES, S. and OWEN, M.R., 2004. SIAM Journal on Applied Dynamical Systems. 3(4), 574-600
  • COOMBES, S., HINCH, R. and TIMOFEEVA, Y., 2004. Progress in Biophysics and Molecular Biology. 85(2-3), 197-216
  • TIMOFEEVA, Y. and COOMBES, S., 2004. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. VOL 70(NUMB 6), 062901
  • CHIK, D. T. W., COOMBES, S. and WANG, Z. D., 2004. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. VOL 70(PART 1), 011908
  • COOMBES, S. and BRESSLOFF, P.C., 2003. Physical Review Letters. 91(2), 028102
  • COOMBES, S., LORD, G. J. and OWEN, M. R., 2003. Physica D - Nonlinear Phenomena. VOL 178(NUMBER 3-4), 219-241
  • COOMBES, S., 2003. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. VOL 67(PART 4), 041910
  • TIMOFEEVA, Y. and COOMBES, S., 2003. A Stochastic Fire-Diffuse-Fire Model of Ca^2^+ Release FORMA -TOKYO-. VOL 18(PART 1), 53-58
  • COOMBES, S. and TIMOFEEVA, Y., 2003. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. VOL 68(PART 2), 021915
  • DENMAN-JOHNSON, M. and COOMBES, S., 2003. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. VOL 67(PART 5), 051903
  • JAMES, M. P., COOMBES, S. and BRESSLOFF, P. C., 2003. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. VOL 67(PART 5), 051905
  • BRESSLOFF, P.C. and COOMBES, S., 2003. Synchronization of synaptically-coupled neural oscillators. In: Epilepsy as a dynamic disease Springer-Verlag, Heidelberg.
  • TIMOFEEVA, Y. and COOMBES, S., 2003. Journal of Mathematical Biology. VOL 47(PART 3), 249-269
  • LORD, G. J. and COOMBES, S., 2002. Physica D - Nonlinear Phenomena. VOL 161(NUMBER 1-2), 1-20
  • BRESSLOFF,P.C. and COOMBES,S., 2001. Mathematical reduction techniques for modeling biophysical neural networks. In: POZNANZKI, R.R., ed., Biophysical Neural Networks: Foundations of integrative neuroscience Mary Ann Liebert, Inc., New York, USA. 215-260
  • COOMBES, S, OWEN, M R and SMITH, G D, 2001. Mode locking in a periodically forced integrate-and-fire-or-burst neuron model. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 64(4 Pt 1), 041914
  • COOMBES, S., 2001. Physica D - Nonlinear Phenomena. VOL 160(NUMBER 3-4), 173-188
  • COOMBES, S., 2001. Mathematical Biosciences. VOL 170(NUMBER 2), 155-172
  • COOMBES, S., 2001. Bulletin of Mathematical Biology. VOL 63(PART 1), 1-20
  • COOMBES, S. and BRESSLOFF, P. C., 2000. SIAM Journal on Applied Mathematics. VOL 61(PART 2), 432-453
  • BRESSLOFF, P. C. and COOMBES, S., 2000. Neural Computation. VOL 12(PART 1), 91-130
  • BRESSLOFF, P. C. and COOMBES, S., 2000. SIAM Journal on Applied Mathematics. VOL 60(PART 3), 820-841
  • COOMBES, S. and OSBALDESTIN, A. H., 2000. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. VOL 62(PART 3), 4057-4066

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