Multiple bifurcations generated by mode interactions in a reaction–diffusion problem

Abstract

We study multiple bifurcations in a system of reaction–diffusion equations defined on a unit square with Robin boundary conditions. First we investigate linear stabilities of the system at the uniform steady state solution. Then we discuss how multiple bifurcations can be generated by mode interactions of the system, and how these multiple bifurcations can be preserved in the associated discrete system. A continuation-unsymmetric Lanczos algorithm is described to trace discrete solution curves. Numerical experiments on the Brusselator equations are reported.