STABILITY OF T-PERIODIC SOLUTION ON THE EXTENDED SIMPLIFIED BRUSSELATOR MODEL

Abstract

Brusselator model is a very typical autocatalytic reaction diffusion system. The bifurcation of steady-states of Brusselator model can be used to explain spot patterns of certain animals such as leopard and jaguar. Periodic patterns can be found throughout whole natural world, so it is very interesting to study patterns generated by the bifurcation of periodic solutions in extended Brusselator (EB) model, which extends Brusselator to T-periodic coefficients. In this paper, we study extended simplified Brusselator (ESB) model, which is EB model without diffusion terms. We find a unique T-periodic solution x0(t) in the strictly positively invariant region [Formula: see text] and prove its stability. This result establishes a foundation to study the bifurcation of EB model from x0(t). We also develop techniques of using degree theory and Floquet theory to analyze existence, uniqueness and stability of a periodic solution.