G.E. Hutchinson's delay logistic system with symmetries and spatial diffusion

In this paper 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©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, are listed in Tables 1–6.