Anti-synchronization of nonlinear dynamical systems based on Gardano's method

This letter derives new results for the design of nonlinear controller for the anti-synchronization of two non-identical 4D hyperchaotic systems. The stability results are established using two analytical approaches; Lyapunov's second method and Gardano's method. Since the constructing positive definite Lyapunov functions are not required for the Gardano method, the nonlinear control strategy is very effective and convenient to realize the anti-synchronization of non-identical hyperchaotic systems. Furthermore, Gardano method is used to overcome some problem in Lyapunov method which helps to achieve the convergence of error dynamics easily. This proposed method has certain significances for reducing the effort and complexity of controller implementation. Finally, numerical simulations are given to illustrate and verify the results.