Estimating the Globally Exponentially Attractive Set and Positively Invariant Set for the Qi Chaotic System and its Applications to Chaos Synchronization

The globally exponentially attractive set and synchronization problem of the Qi chaotic system was researched. Firstly, based on the definition of globally exponentially attractive set and constructing a generalized positive definite Lyapunov functions with radially unbound respect with to the parameters of the system, and employing the continuous extension principle, a new cylinder estimation of the globally exponentially attractive set and positive invariant set of the Qi chaotic system was given without existence assumptions. Secondly, linear feedback approach was used to realize the globally exponential synchronization of two chaotic systems and a sufficient algebraic criterion for the globally exponential synchronization of two chaotic systems is obtained analytically. Finally, simulations are conducted to prove synchronous validity and these figures of synchronous errors are given. The numerical simulation results indicated the effectiveness of the proposed methods.