title: Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay.
abstract: The dynamic regimes in networks of four almost identical spike oscillators with pulsatile coupling via inhibitor are systematically studied. We used two models to describe individual oscillators: a phase-oscillator model and a model for the Belousov-Zhabotinsky reaction. A time delay τ between a spike in one oscillator and the spike-induced inhibitory perturbation of other oscillators is introduced. Diagrams of all rhythms found for three different types of connectivities (unidirectional on a ring, mutual on a ring, and all-to-all) are built in the plane C(inh)-τ, where C(inh) is the coupling strength. It is shown analytically and numerically that only four regular rhythms are stable for unidirectional coupling: walk (phase shift between spikes of neighbouring oscillators equals the quarter of the global period T), walk-reverse (the same as walk but consecutive spikes take place in the direction opposite to the direction of connectivity), anti-phase (any two neighbouring oscillators are anti-phase), and in-phase oscillations. In the case of mutual on the ring coupling, an additional in-phase-anti-phase mode emerges. For all-to-all coupling, two new asymmetrical patterns (two-cluster and three-cluster modes) have been found. More complex rhythms are observed at large C(inh), when some oscillators are suppressed completely or generate smaller number of spikes than others.
authors: Centre for Nonlinear Chemistry, Chemical-Biological Institute, Immanuel Kant Baltic Federal University, A. Nevskogo str. 14A, Kaliningrad, 236041, Russia. vladimir.klinshov@ipfran.ru.
authors: Vladimir K
authors: VK
authors: Vanag
authors: Pavel S
authors: PS
authors: Smelov
authors: Vladimir V
authors: VV
authors: Klinshov