Analysis of the Qi three dimensional chaotic system

Abstract: This paper applies the center manifold theorem to reduce the dimensions of the Qi three-dimensional system. Local bifurcation phenomena are analyzed, including the pitchfork and Hopf bifurcations of the chaotic system. The Poincaré map is also investigated. The analyses demonstrate the rich dynamics of the Qi chaotic system. Finally, the frequency spectral analysis shows that the system has a broad frequency bandwidth, which is desirable for engineering applications such as secure communications

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results