Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters

This paper considers the anti-synchronization problem between hyperchaotic Rِssler system and hyperchaotic Lorenz system. Two anti-synchronization schemes of them are proposed. Active control is applied when system parameters are known and adaptive control is employed when system parameters are unknown or uncertain. Controllers and update laws of parameters are designed based on Lyapunov stability theory. In both cases, sufficient conditions for the anti-synchronization are obtained analytically. Finally, numerical simulations are provided to show the effectiveness of the proposed schemes.