Analysis of chaotic systems using the cell mapping approach

Abstract

Chaotic motions in deterministic nonlinear systems are an important topic both from a theoretical and a practical point of view. In particular, there have been many studies of systems which yield bounded nonperiodic trajectories converging to attractors of a rather complicated nature, so-called strange attractors. Their existence was demonstrated in a class of nonlinear oscillators with periodic forcing which occur in electric circuit theory and mechanics. The determination of the domain of attraction of such attractors, depending on the parameters, is an interesting problem. It is shown, that the cell mapping approach, i.e., a discrete version of a Poincare map, represents a very efficient method for analyzing this problem.