Spiking networks and the Haken–Lighthouse model
Event-driven spiking dynamics, synchrony, waves and pattern formation, and their reduction to population descriptions.
Research
My research uses ideas from nonlinear dynamics, applied mathematics and mathematical physics to understand how neuronal activity gives rise to collective behaviour and computation. A central interest is connecting the dynamics of individual neurons and their interactions to patterns, waves and rhythms in large networks.
Recent work emphasises spiking-network dynamics and the effects of axonal conduction delays, including delays that change with neural activity. Related interests include neural fields and population models, brain rhythms, and the mathematics of excitable cellular systems.
White-matter computation and adaptive delays
Activity-dependent conduction delays, phase locking and network reorganisation through white-matter plasticity.
Neural fields and population models
Spatial patterns, travelling waves, neural masses and links between collective dynamics and connectivity.
Brain rhythms and thalamo-cortical dynamics
Mechanisms of oscillations, rebound and synchronisation, with connections to EEG and MEG.
Cellular signalling and excitable media
Calcium waves, fire-diffuse-fire dynamics, active dendrites and spatially organised cellular excitation.
Coupled oscillators and phase–amplitude reduction
Synchronisation and bifurcations in oscillator networks, phase–isostable methods, and delayed interactions.
Research group
PhD students
- Matthew James : Synaptic travelling waves in integrate-and-fire neural networks PhD 2003
- Yulia Timofeeva : Calcium waves and oscillations PhD 2004
- Matthew Denman-Johnson : Dynamics of synaptically coupled McKean neurons PhD 2005
- Margarita Zachariou : Neurobiology of sensory gating: a neural network study Phd 2008
- Nikola Venkov : Dynamics of neural field models Phd 2009
- Carl-Magnus Svensson : Branching dendrites with active spines Phd 2009
- Jonathan Laudanski : Neural processing of sound in the auditory system Phd 2010
- Jaroslav Hlinka : Studying spontaneous brain activity with neuroimaging methods and mathematical modelling Phd 2010
- Ana-Maria Gheorghe : Understanding spiking and bursting electrical activity through piece-wise linear systems Phd 2011
- Helmut Schmidt : Interface dynamics in 2D neural field models Phd 2012
- Kyle Wedgwood : Dynamical systems techniques in the analysis of neural systems PhD 2013
- Ruth Smith : Amplitude equations for pattern forming neural systems PhD 2014
- Georgina Fenton : Neural network interactions underlying emotional learning & memory: Integrating experimental & theoretical approaches PhD 2015
- Mayte Bonilla Quintana : Theoretical Neuroscience: From long wavelength cortical patterning to spatial navigation PhD 2017
- Aytül Gökçe : The dynamics of Amari type neural field models on finite domains PhD 2017
- Aine Byrne : Next Generation neural activity models: Bridging the gap between mesoscopic and microscopic brain scales PhD 2017
- Alban Levy : Machine Learning for Neural Coding of Sound Envelopes: Slithering from Sinusoids to Speech PhD 2018
- Michael Forrester : Modelling of large-scale brain network dynamics PhD 2020
- Mustafa Sayli : Nonsmooth dynamical systems: from nodes to networks PhD 2021
- Charline Tessereau : Reinforcement Learning Approaches to Rapid Hippocampal Place Learning PhD 2021
- Sunil Modhara : Brain Dynamics From Mathematical Perspectives: A Study of Neural Patterning PhD 2022
- Abigail Cocks : The dynamics of neural fields and applications to vision PhD 2023
- Sammy Petros : The numerical solution of neural field models posed on realistic cortical domains PhD 2023
- James Ross : Mathematical Neuroscience: From Neural Fields to Neuroimaging PhD 2025
- Oliver Cattell : Epilepsy as a dynamic disease PhD 2026
- Robert Allen : Phase-isostable descriptions of coupled oscillator networks PhD 2026
- Angelica Pozzi : Thalamo-cortical modelling Yr 3
- Grace Jolly : Waves and patterns in heterogeneous neural media Yr 2
- Emanuil Hristov : Neurocomputation in networks with plastic delays Yr 2
- Rifah Tasnia: Mathematical Neuroscience in Mental Health Yr 1 (2026 start)
Postdoctoral researchers
- Yulia Timofeeva : Branching dendrites with active spines 2004-2007
- James Smith : Glucose metabolism 2006
- Rüdiger Thul : A fire-diffuse-fire framework for the functional organisation of cellular calcium signals 2006-2009
- Carl-Magnus Svensson : Building contours from edges in mid-level vision 2009-2011
- Sid Visser : Mathematical neuroscience 2013-2015
- Yi Ming Lai : Threshold Networks 2017-2020
- Michael Forrester : Using next generation neural mass models to understand the effects of neuromodulation on large scale brain dynamics 2020-2022
- Mustafa Sayli : White Matter Networks 2021-2023
- Stefan Ruschel : White Matter Computation: Utilising axonal delays to sculpt network attractors 2026-2028
Research funding
- 1999 Nuffield Foundation A Computational Neurodynamics of Integrate-and-Fire Oscillators [equipment grant] £4,000
- Royal Society Travel grant: SIAM Dynamical Systems Conference, Snowbird, Utah £885
- 2000 LMS Travelling waves in neural dendrites (small grant scheme 4) £336
- 2001 Royal Society Travel grant: SIAM Dynamical Systems Conference, Snowbird, Utah £800
- 2002 EPSRC Advanced Research Fellowship: Synaptic travelling waves . Final Report . £235,145
- Royal Society travel grant: European Conference on Mathematical Biology, Milan £700
- 2003 Nuffield Foundation Neuronal Dynamics: Sensitivity, Reliability and Arnol'd Tongues [summer studentship] £1,570
- Royal Society Directed percolation and calcium waves [equipment grant] £8,968
- EPSRC Branching dendrites with active spines (with Gabriel Lord ) [post-doc and student] £110,000
- 2004 ICIAM '99 Fund Modelling neuronal dendritic trees (with Gabriel Lord ) [workshop] £2,500
- EPSRC Math Bio Network Mathematical Neuroscience (with Gabriel Lord ) [conference] £5,000
- LMS International visitor grant [ Dr Carlo Laing ] £1,200
- 2005 EPSRC A fire-diffuse-fire framework for the functional organisation of cellular calcium signals (with Dr Martin Bootman ) £140,372
- EPSRC Theory and applications of coupled cell networks ( P C Matthews , S Coombes, P Ashwin , J Dawes and M Golubitsky ) £14,935
- BRC Nottingham Combined EEG & functional MRI to study the functional organisation of brain microstates associated with altered levels of consciousness ( Dorothee Auer , Jonathan Hardman , Steve Coombes) £50,000
- UK-Texas DTI Initiative The Neuron as a Network (with Steve Cox , Kresimir Josic & Costa Colbert ) £9,000
- 2006 EPSRC Mathematical modelling of cellular calcium signals [workshop] £4,415
- 2007 Nuffield Foundation Mathematical modelling of thalamo-cortical oscillations [summer studentship] - Report £1,360
- BBSRC Cell Signalling Network (with Markus Owen and Nick Monk ) £90,000
- EPSRC Mathematical Neuroscience Network (with Yulia Timofeeva ) £157,000
- 2008 Royal Society Travel grant: HBM 2008 £900
- LMS Visitors grant for Dr Carlo Laing £1,200
- British Council The role of noise and geometry in cellular signalling (with Ruediger Thul ) £2,250
- Wellcome Building contours from edges in mid-level vision (as Co-I with Jon Peirce ) £242,000
- 2009 LMS Visitors grant for Dr Carlo Laing £1,200
- Bridging the Gaps Complex System Dynamics: A neural network approach (with Noah Russell ) £15,000
- 2011 EPSRC Neurodynamics: a workshop on heterogeneity, noise, delays, and plasticity in neural systems (with Yulia Timofeeva and Mark van Rossum ) £30,000
- 2012 EC Marie Curie Initial Training Network - NETT €5.3M
- 2012 BBSRC Ectopic transmission in the cerebellar cortex (as Co-I with Tom Bellamy ) £300,000
- 2016 EPSRC Threshold Networks (with Rüdiger Thul ) £336,000
- 2021 EPSRC White Matter Networks (with Stamatios Sotiropoulos and Stephen Jackson ) £200,000
- 2025 Leverhulme White Matter Computation: Utilising axonal delays to sculpt network attractors (as Co-I with Rachel Nicks ) £369,202