Analysis of a four-variable model of coupled chemical oscillators

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Abstract
A simple model for the coupling of two chemical oscillators is proposed. The model consists of twotwo-variable subsystems, each of which gives rise to a ‘‘cross-shaped phase diagram’’ containing two different steady states plus regions of bistability and of oscillation. The subsystems are coupled by diffusion of both species. Extensive numerical simulations reveal that when one subsystem is in the bistable and the other in the oscillatory region of the parameter space, coupling can result in birhythmicity, period doubling, and chaos. When both subsystems are in the oscillatory region, the coupled behavior is even richer, including quasiperiodicity, entrainment, chaos, and phase death (cessation of oscillations), with various hysteresis phenomena between these modes of behavior. The relation of these observations to behavior found experimentally in coupled chemical oscillators is discussed.