Synchronization and anti-synchronization of a hyperchaotic Chen system

Based on the active control theory, synchronization and anti-synchronization between two identical chaotic systems is investigated. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in chaotic systems. Numerical simulations are performed for Chen hyperchaotic dynamical system to demonstrate the effectiveness of the proposed control strategy.