On Stable and Unstable Periodic Solutions of N-Dimensional Discrete Dynamical Systems

Abstract

This paper presents a methodology to analytically predict the stable and unstable periodic solutions for n-dimensional discrete dynamical systems. 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 relative to the positive and negative mapping structures are presented. A discrete dynamical system with the Henon map is investigated as an example. The Poincare mapping sections relative to the Neimark bifurcation of periodic solutions are presented, and the chaotic layers for the discrete system with the Henon map are observed.