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 u...

This paper presents the outcome of power series analysis in the framework of the Asymptotic Numerical Method. We theoretically demonstrate and numerically evidence that the emergence of geometric power series in the vicinity of simple bifurcation points is a generic behavior. So we propose to use this hallmark as a bifurcation indicator to locate and compute very efficiently any simple bifurcat...