Experimental investigation of a unidirectional network of four chemical oscillators pulse-coupled through an inhibitor

Abstract

Dynamical synchronous modes in a network of four nearly identical chemical oscillators unidirectionally coupled via inhibitory pulse coupling with time delay τ (when a spike in one oscillator inhibits the next oscillator in the circle after time delay τ), are obtained experimentally. The Belousov–Zhabotinsky reaction is used as a chemical oscillator. The existence of four main modes is confirmed experimentally: in-phase (IP) oscillations; an anti-phase (AP) mode, in which any two neighboring oscillators have a phase shift equal to half of global period T; a walk mode (W), in which oscillators produce consecutive spikes in the direction of the connection with a phase shift between neighboring oscillators equal to T/4; and a walk-reverse mode (WR), when the oscillators produce consecutive spikes (with phase shift T/4), but in the direction opposite the connections (the mode opposite to the W mode). In addition to the main modes, OS modes in which at least one of the four oscillators is suppressed, and “2+1+1” modes in which two neighboring oscillators produce spikes simultaneously and the phases of the third and the fourth oscillators are shifted by T/3 and 2T/3, respectively, are found. It is shown that the modes found experimentally correspond to those found in simulations.