Two-Dimensional Manifolds of Controlled Chen System

Abstract

We focus on the two-dimensional stable manifold of Chen system. Based on the Chen system, a new system with nonlinear control is put forward, which exhibits brand new dynamical phenomena such as the coexistence of heteroclinic orbits with periodic solutions, or two new attractors. The emergence of manifold surface is found by tangential self-intersection. The two-dimensional unstable manifold of saddle-focus tends to another equilibrium solution asymptotically, the underlying heteroclinic bifurcation and the “twins” unstable manifolds are bulit from two saddle-focus respectively.