Hybrid Synchronization of Hyperchaotic Wang-Chen and Hyperchaotic Lorenz Systems by Active Non-linear Control

This study investigates the hybrid synchronization of identical hyperchaotic Wang-Chen systems, identical hyperchaotic Lorenz systems and non-identical hyperchaotic Wang-Chen and Lorenz systems. The hyperchaotic Wang-Chen system and hyperchaotic Lorenz system are important models of hyperchaotic systems. Hybrid synchronization of the hyperchaotic systems addressed in this study is achieved through the synchronization of the 1st and 3rd states of the master and slave systems and anti-synchronization of the 2nd and 4th states of the master and slave systems. Active nonlinear control is the method used for the hybrid synchronization of hyperchaotic Wang-Chen and Lorenz systems and the stability results are established using Lyapunov stability theory. Since, the Lyapunov exponents are not required for these calculations, the proposed method is quite effective and convenient to achieve hybrid synchronization of the hyperchaotic systems addressed in this study. Numerical simulations are provided to illustrate the effectiveness of the various synchronization schemes proposed in this study.