Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

• Published in: Physical chemistry chemical physics : PCCP 2016-02, Vol.18 (7), p.559-552
• Main Authors: Vanag, Vladimir K, Smelov, Pavel S, Klinshov, Vladimir V
• Format: Article
• Language: English
• ISSN: 1463-9076; 1463-9084
• DOI: 10.1039/c5cp06883e

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. The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.