Abstract

In this paper, a methodology to analytically predict the stable and unstable periodic solutions forn-dimensional discrete dynamical systems is applied to investigate the Henon map. The positive and negative iterative mappings of discrete maps are introduced for the mapping structure of the periodic solutions. The complete bifurcation and stability of the stable and unstable periodic solutions with respect to the positive and negative mapping structures is given. The Poincare mapping sections of the Neimark bifurcation of periodic solutions is presented, and the chaotic layers for the discrete system with the Henon map are observed.

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