Abstract
The synchronization of chaotic real systems or chaotic complex systems has been extensively discussed in previously conducted studies. However, much is not known regarding the synchronization between complex drive systems and real response systems. This study investigates a novel modulus synchronization between a hyperchaotic real system and its corresponding complex system. The systems are designed and their dynamical properties including invariance, dissipation, equilibria, Lyapunov exponents and the spectrum of them, as well as hyperchaotic attractors are analyzed in detail. Moreover, the adaptive controller is also developed based on Lyapunov stability theory. Furthermore, the numerical simulation experiments verify the effectiveness of our idea.
Highlights
Pecora and Carroll are among the pioneers that studied chaos synchronization in 1990 [1]
By the motivation of the synchronization of chaotic real systems, the synchronization of chaotic complex systems has been a subject of increasing research interest
We investigate a hyperchaotic real system and its corresponding complex system, which are applied to modulus synchronization
Summary
Pecora and Carroll are among the pioneers that studied chaos synchronization in 1990 [1]. Li et al.: Modulus Synchronization of a Novel Hyperchaotic Real System and Its Corresponding Complex System systems and complex response systems, or real drive systems and complex response systems It is a meaningful and interesting problem to design synchronization for a complex drive system and a real response system. By applying Lyapunov stability theory, the adaptive controller is designed to achieve synchronization between a complex drive system and a real response system.
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