Active Control Design for the Hybrid Synchronization of Arneodo and Rössler Chaotic Systems

This paper investigates the hybrid chaos synchronization of identical Arneodo systems (1981), identical Rössler systems (1976) and non-identical Arneodo and Rössler systems. In hybrid synchronization of chaotic systems, one part of the systems is synchronized, while the other part is anti-synchronized so that complete synchronization (CS) and anti-synchronization (AS) co-exist in the systems. The co-existence of CS and AS is very useful in secure communication and chaotic encryption schemes. Active nonlinear control method is used for hybrid synchronization of the Arneodo and Rössler systems and the synchronization results have been proved using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is very effective and convenient to achieve hybrid synchronization of the Arneodo and Rössler systems. Numerical simulations are shown to verify the results.