Anti-Synchronization of the Four-Dimensional Hyperchaotic System with Uncertain Parameters Via Adaptive Control

In this paper, an adaptive control scheme is presented to study the anti-synchronization behavior between two identical four-dimensional hyperchaotic systems with unknown parameters. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Based on Lyapunov stability theory, an adaptive anti-synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. Numerical simulations are performed for four-dimensional hyperchaotic systems to demonstrate the effectiveness of the proposed control strategy.