@ 1995 Kluwer Academic Publishers. Printed in the Netherlands. Parameter Variation Methods for Cell Mapping

Abstract. In the study of nonlinear dynamic systems, the influence of system parameters onthe long term behaviour plays an important role. In this paper, parameter variation methods are presented which can be used when investigating a nonlinear dynamic system by means of simple or interpolated cell mapping. In the case of coexisting attractors, the proposed methods determine the evolution of the basin boundaries when a system parameter is varied. Application of the methods toa modified Duffing equation is performed. It is concluded that the proposed methods are very efficient and accurate. Key words: Cell mapping, continuation, basins of attraction, chaos. 1