Analysis of Nonlinear Reaction–Diffusion Systems by the Perturbation Method: Conditions of Application, Construction of Solutions, and Bifurcation Analysis

Abstract

For nonlinear systems of reaction–diffusion type, we propose a technique for the construction and analysis of solutions based on the method of small parameter. The proposed technique enables us not only to analytically obtain approximate quasiharmonic low-amplitude solutions appearing as a result of bifurcations of spatially homogeneous states of the system but also to determine the type of bifurcation in the system. Examples of application of this approach to the analysis of bifurcations and the construction of solutions of a specific mathematical reaction–diffusion model are given.