An algorithm based on variable feedback to synchronize chaotic and hyperchaotic systems

In recent years, the subject of how to synchronize chaotic and hyperchaotic systems has attracted much attention due to its theoretic interest and potential applications to secure communications. Various approaches have been proposed and pursued. In this work, an algorithm based on variable feedback is developed analytically and applied to a nine-dimensional Lorenz system numerically. One finds that the proposed method can be applied to chaotic systems with one or more Lyapunov exponents. It is also demonstrated that the given method can be further simplified for concrete systems.