Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay

Abstract

Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov–Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory–inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio. Analogously to in-phase and anti-phase oscillations for 1 : 1 resonance, a similar phase locking exists for 1 : 2 resonance in the case of inhibitory coupling. For excitatory coupling, a bursting regime is found. The number of spikes in a single burst can be tuned by both the frequency ratio and time delay. For excitatory–inhibitory coupling, a region where one oscillator is suppressed (OS zone) has been found. Boundary of the OS zone depends on the frequency ratio. For weakly coupled oscillators, Farey sequence has been found for excitatory–inhibitory and mutual excitatory coupling.