Phase plane approach to cooperative rhythms in neuron motifs with delayed inhibitory synapses

Abstract

The phenomenon of burst synchronization is analyzed in binary and ternary motifs consisting of Rulkov map neurons coupled via delayed inhibitory synapses. We determine the particular roles and the interplay between the intrinsic neuron and synaptic parameters, as well as the network topology. The developed method, resting on exactly obtaining the curves that guide the neuron orbits in the phase plane, enabled us to identify the motif-specific mechanisms of how the synchronized rhythms emerge, even in the presence of strong delay. It is explained why the location of the parameter space domain optimal for burst synchronization gets shifted with different motif architectures. Further, it is suggested how for each motif a distinct cooperative rhythm may be singled out, that is absent on any of the other considered motifs. © 2010 Europhysics Letters Association.