Hybrid Synchronization of Hyperchaotic Lorenz and Hyperchaotic Chen Systems via Active Control

This study investigates the hybrid synchronization of Hyperchaotic Lorenz and Chen Systems via adaptive control. Explicitly, researchers derive new results for the hybrid chaos synchronization of identical Hyperchaotic Lorenz Systems, identical Hyperchaotic Chen Systems and non-identical Hyperchaotic Lorenz and Chen Systems. In this study, Researchers assume that the parameters of both master and slave systems are unknown and we devise adaptive hybrid synchronization schemes using the estimates of parameters for both Master and Slave Systems. The adaptive hybrid synchronization results derived in this study are established using Lyapunov Stability Theory. Since, the Lyapunov exponents are not required for these calculations, the proposed Adaptive Control Method is very effective and convenient to achieve hybrid synchronization of identical and non-identical Hyperchaotic Lorenz and Chen Systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive hybrid synchronization schemes for the hyperchaotic systems addressed in this study.