ABSTRACT

In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of identical hyperchaotic Lorenz systems (2007), identical hyperchaotic Chen systems (2010) and non-identical hyperchaotic Lorenz and hyperchaotic Chen systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive synchronizing schemes using the estimates of parameters for both master and slave systems. Our adaptive synchronization results derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical hyperchaotic Lorenz and hyperchaotic Chen systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the hyperchaotic systems addressed in this paper.