Original research articleHybrid chaos synchronization between two different hyperchaotic systems via two approaches

This paper deals with the hybrid synchronization between two non-identical 4D hyperchaotic systems; Modified hyperchaotic Pan system and hyperchaotic Liu system via nonlinear control technique, based on two analytical approaches; Lyapunov's second method and Gardano's method. We compare between the two approaches and notice the Lyapunov stability theory is need to modify a quadratic Lyapunov function at some time, and furthermore, it's failing in other cases. For this reason, this Letter is using a new analytical approach which doesn't need any modified, what distinguishes this method and makes it better than the Lyapunov approach. Theoretical and numerical simulations are given to illustrate and verify the results.