Asymptotically stable heteroclinic cycles in discrete-time -equivariant cubic dynamical systems

Abstract

We consider a discrete-time -equivariant cubic dynamical system depending upon a real parameter. The system under consideration is a particular case of a discrete analogue to the principal -equivariant differential equations. We rigorously prove that the system has an asymptotically stable heteroclinic cycle, relatively to an open subset of a compact subspace of the plane, for values of the parameter in the interval . We explore properties of the omega-limit sets for the points attracted by the heteroclinic cycle.