Transitions between nonsymmetric and symmetric steady states near a triple eigenvalue

Abstract

We examine the existence of nonuniform steady-state solutions of a certain class of reaction-diffusion equations. Our analysis concentrates on the case where the first bifurcation is near a triple eigenvalue. We derive the conditions for a continuous transition between nonsymmetric and symmetric solutions when the bifurcation parameter progressively increases from zero. Finally, we give an example of a four variables model which presents the possibility of a triple eigenvalue.