Hopf Bifurcation Analysis of a Chaotic System

This paper is devoted to studying the stability of unique equilibrium point and occurrence Hopf bifurcation as well limit cycles a three-dimensional chaotic system. We characterize parameters for which takes place at point. In addition, system has only one . It was proved that  is asymptotically stable unstable when  and , respectively. Moreover, cyclicity system, two techniques are used dynamics on center manifold Liapunov quantities. shown most can be bifurcated from origin. All results presented in this have been verified by program via Maple software.