Modified function projective lag synchronization of hyperchaotic complex systems with parameter perturbations and external perturbations

In this paper, a novel synchronization method of modified function projective lag synchronizations (MFPLS) between identical and nonidentical hyperchaotic complex nonlinear systems with parameter perturbations and external perturbations is proposed. In the method, the states of two hyperchaotic complex systems with parameter perturbations and external perturbations are asymptotically lag synchronized up to a desired scaling function matrix, and all the perturbations in the parameters asymptotically converge to zero. Base on the Lyapunov stability theory, the adaptive controller and updating laws of parameter perturbations are designed to achieve MFPLS between the drive and response systems. Theoretically the proof that the drive and response system will asymptotically lag synchronization and numerical simulations verify the feasibility and effectiveness of the proposed scheme.