Estimations On Globally Exponentially Attractive Set And Positive Invariant Set Of Lü System

After discovery of the famous Lorenz system and Chen system.In 2002,Lü et al.found a very important chaotic system between the Lorenz system and Chen system that called Lü system.In the study of chaotic systems,the estimates of the ultimate boundedness or the attractive set have great important theoretical significance and practical application.If a chaotic system have attracted global compact set inside the space,equilibrium position,periodic solutions,almost periodic solution,chaos attractor can't exist without it.From the application point of view,the estimates of the ultimate boundedness and the concrete ultimate bounded boundary value,are often applied to chaos control,chaos tracking and chaos synchronization.As a famous chaotic system,accurate estimations for attractive set of Lü system is important.In this paper we give an estimation on globally exponentially attractive set and positive invariant set of Lü system by constructing several generalized positive Lyapunov functions.Specifically,the state space can be divided into several regions,and for each region we construct an appropriate generalized positive definite function and obtain the estimate by combining with classical technique.Finally through the simulation the validity of the estimates is shown.