Spike train dynamics underlying pattern formation in integrate-and-fire oscillator networks

A dynamical mechanism underlying pattern formation in a spatially extended network of integrate-and-fire oscillators with synaptic interactions is identified. It is shown how in the strong coupling regime the network undergoes a discrete Turing-Hopf bifurcation of the firing times from a synchronous...

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Main Authors: P.C. Bressloff, S. Coombes
Format: Article
Language:English
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Mathematical Sciences not elsewhere classified
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Summary:A dynamical mechanism underlying pattern formation in a spatially extended network of integrate-and-fire oscillators with synaptic interactions is identified. It is shown how in the strong coupling regime the network undergoes a discrete Turing-Hopf bifurcation of the firing times from a synchronous state to a state with periodic or quasiperiodic variations of the interspike intervals on closed orbits. The separation of these orbits in phase space results in a spatially periodic pattern of mean firing rate across the network that is modulated by deterministic fluctuations of the instantaneous firing rate.