Diffusive instability near Hopf bifurcation for exponentially autocatalyzed reaction-diffusion system

Abstract

The analysis of an exponentially autocatalyzed reaction-diffusion system near the Hopf bifurcation point has been carried out using a reductive perturbation approach to obtain a description in terms of the Ginzburg-Landau equation. The conditions for the occurrence of instability, in the presence and absence of diffusion, leading to Hopf bifurcation are also derived. The nature of the governing equations leads to multi-valued instability conditions and eventually results in more than one region in parameter space where instability of uniform oscillations due to diffusion is possible.