Hybrid Chaos Synchronization of Uncertain Lorenz-Stenflo and Qi 4-D Chaotic Systems by Adaptive Control

Abstract

This paper investigates the hybrid chaos synchronization of uncertain 4 -D chaotic systems, viz. identical Lorenz-Stenflo (LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non identical LS and Qi systems. In hybrid chaos synchronization of master and slave systems, the odd states of the two systems are completely synchronized, while the even states of the two systems are anti synchronized so that complete synchronization (CS) and anti -synchronization (AS) co-exist in the synchronization of the two systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for the hybrid chaos synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes 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 achieve hybrid synchronization of identical and non-identical LS and Qi systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for theidentical and non-identical uncertain LS and Qi 4-D chaotic systems.