Center manifold theory for discrete dynamical systems

Abstract

Using the center manifold theory for maps, we derive a theorem for the existence of backward bifurcation at bifurcation points of discrete dynamical systems. This theorem is an analogue of a theorem in [3] for continuous dynamical systems. We discuss applications to discrete dynamical systems in general [2], but more specifically those arising as dicretisations of continuous dynamical systems via the nonstandard finite difference method [1].