Haibo Ruan

Symmetric Hopf Bifurcation in n-Species Hutchinson Model

Haibo Ruan
Dept. of Math and Stat Sciences, University of Alberta

In this talk we apply the equivariant degree method to a Hopf bifurcation problem in a symmetric system of delayed functional parabolic partial differential equations. The equivariant spectral properties of the linearized system are instantaneously translated, with the assistance of a specially developed Maple package, into a bifurcation invariant providing symmetric classification of the bifurcating branches. This procedure is applied to a symmetric Hutchinson model of an $n$ species ecosystem in a heterogeneous environment. Computational results, indicating the existence, multiplicity and symmetric classification of the solutions, will be presented.