Integrate-and-fire neural networks

The dynamics of coupled oscillator arrays has been the subject of much recent experimental and theoretical interest. Example systems include Josephson junctions, lasers, oscillatory chemical reactions, heart pacemaker cells, central pattern generators and cortical neural oscillators. In collaboration with Paul Bressloff I am studying the dynamics of integrate-and-fire systems neurons with delayed interactions. We have been developing group theoretic techniques for analysing bifurcations in a ring of such oscillators with the aim of understanding the effects of the range of spatial interactions and the size of the delays. We have also been studying travelling waves on oscillator chains and the occurrence of instabilities as the strength of coupling is increased. Although studying the effects of delays and finite-range interactions is motivated by neurobiology (specifically the work of Alan Roberts on locomotion), such features could also be relevant to physics applications such as Josephson junction arrays (in regimes where the lumped circuit description is no longer valid) and SQUID arrays. More recently the spike train dynamics underlying pattern formation and chaos in integrate-and-fire networks has been investigated.

Relevant publications:

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)
S Coombes, R Thul and K C A Wedgwood 2012 Nonsmooth dynamics in spiking neuron models, Physica D, Vol 241, 2042–2057
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
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 2000 Dynamics of strongly-coupled spiking neurons, Neural Computation, Vol 12, 91-129
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
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 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 Intrinsic modulation of pulse-coupled integrate-and-fire neurons, Phys. Rev. E., Vol 56, No 5, 5809-5818