Dynamic modes in a network of five oscillators with inhibitory all-to-all pulse coupling.

Abstract

The dynamic modes of five almost identical oscillators with pulsatile inhibitory coupling with time delay have been studied theoretically. The models of the Belousov-Zhabotinsky reaction and phase oscillators with all-to-all coupling have been considered. In the parametric plane Cinh-τ, where Cinh is the coupling strength and τ is the time delay between a spike in one oscillator and pulsed perturbations of all other oscillators, three main regimes have been found: regular modes, when each oscillator gives only one spike during the global period T, C (complex) modes, when the number of pulses of different oscillators is different, and OS (oscillations-suppression) modes, when at least one oscillator is suppressed. The regular modes consist of several cluster modes and are found at relatively small Cinh. The C and OS modes observed at larger Cinh intertwine in the Cinh-τ plane. In a relatively narrow range of Cinh, the dynamics of the C modes are very sensitive to small changes in Cinh and τ, as well as to the initial conditions, which are the characteristic features of the chaos. On the other hand, the dynamics of the C modes are periodic (but with different periods) and well reproducible. The number of different C modes is enormously large. At still larger Cinh, the C modes lose sensitivity to small changes in the parameters and finally vanish, while the OS modes survive.