Dynamic analysis and chaos control of a unified chaotic system

Abstract

Two different control methods are proposed in this paper to effectively control the chaotic phenomenon of nonlinear dynamical system. One is a new Hamilton energy feedback control method based on Helmholtz’s theorem, which reduces the Lyapunov exponents value of the system by adjusting the feedback gain for controlling chaos. The other is to control the chaos of the system by using delayed feedback control method. Based on this method, we consider the local asymptotic stability of the equilibrium point of the system, and give conditions for the existence of the Hopf bifurcation of the system and the stability domain of the delay parameters. By using the centre manifold theorem and the Poincare normal form method, specific formulas for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions are derived. Finally, the simulation results show that chaos can be controlled by choosing appropriate time-delay parameters.