Two Dimensional Unstable Manifolds in Chen System and Chen-Lv System

Abstract

The complex dynamics, like chaos induced by period-doubling bifurcation of periodical oscillation phenomena are often examples of nonlinear dynamical science, nevertheless for the Chen system, Chen-Lv system and Lorenz system. The heteroclinic chaos phenomena and the scroll wave chaos phenomena and the Lorenz attractor, respectively of three chaos systems, are often proud complex elements. The two dimensional stable manifold of Lornez system is well known as a successful example of a manifold. The two dimensional unstable manifolds of the Chen system and the Chen-Lv system are computed by the manifold computation method which satisfies the tangency condition. As for the case of the heteroclinic chaos, the twin manifolds are pictured which originate from the two different saddles. Whilst for the case of the Chen-Lv system, the single scroll wave manifold, and the interaction scroll wave manifold and the double scroll wave manifold are computed, which are supposed to be the two dimensional unstable manifolds. The manifold’s picture embodies system symmetry character, which means the manifold has mirror symmetry under the single parameter symmetry.