Control and synchronization of a three-dimensional chaotic system

This paper deals with the control and synchronization of a new three-dimensional continuous quadratic autonomous chaotic system. First, by utilizing adaptive control approaches, the stabilization of unstable equilibrium points of the chaotic system was studied; a sufficient condition of the asymptotical stableilization of equilibrium points was given; the strict proofs were presented in terms of Lyapunov functions and LaSalle invariant principle; then a simple controller was designed; the mismatch synchronization of this chaotic system was investigated by nonlinear feedback control method, and the mismatch synchronization between drive system and respond system was achieved. Several numerical simulations by Matlab were given to show the effectiveness of the proposed chaos adaptive control and mismatch synchronization methods.