Phase-frequency model of strongly pulse-coupled Belousov-Zhabotinsky oscillators

Abstract

We demonstrate that the dynamical behavior of strongly pulse-coupled Belousov-Zhabotinsky oscillators can be reproduced and predicted using a model that treats both the phase and the instantaneous frequency of the oscillators. Model parameters are extracted from the experimental data obtained using a single pulse-perturbed oscillator and are used to simulate the temporal dynamics of a system of two coupled oscillators. Our model exhibits the out-of-phase and anti-phase synchronization and the 1:N and N:M temporal patterns as well as the oscillator suppression that are observed in experiments when the inhibitory coupling is asymmetric. This approach may be adapted to other systems, such as coupled neurons, where the oscillatory dynamics is affected by strong pulses.