Studies On The Global Attractive And Positive Invariant Set Of The Lorenz Families Of Chaotic Systems

In this paper, we review the work in the global attractive set and positive invariant set of chaotic dynamical systems during past years and give an overview of this active field up to now. Based on current knowledge, we mainly employed generalized Lyapunov function to discuss the global attractive set and positive invariant set of the following two chaotic systems:(1) A generalized Lorenz chaotic system: where system parameters a , b , c > 0,ω∈R , m≥0(2) A unified chaotic system where the system parameters 1 29≤α< 2 29The results obtained in this paper extend some existing related conclusions, these results are very important both in chaotic control and synchronization of two systems described above.