Bifurcations in the system of two identical diffusively coupled Brusselators

Abstract

A two-parametrical bifurcation analysis of the dynamics of two identical asymmetrically coupled Brusselators is performed disregarding limitations on the coupling strength and on the parameter choice with respect to Hopf bifurcation. The bifurcations of inhomogeneous steady states and periodic attractors are calculated as functions of the coupling strength and one of the free parameters. Inherent bifurcations for all kinds of solutions and relationships between attractors are established. A four-dimensional scenario of the infinite period bifurcation was considered. Special attention is paid to the spatially inhomogeneous limit cycle which can occupy a large window in a parameter space. It is shown that the structure of the phase diagram is strongly affected by the stiffness, which is a typical feature of real oscillators. The role of the fast variable exchange in the existence of inhomogeneous regimes is discussed.