Abstract
The chaotic complex system is designed from the start of the chaotic real system. Dynamical properties of a chaotic complex system in complex space are investigated. In this paper, a compound synchronization scheme is achieved for four chaotic complex systems. According to Lyapunov stability theory and the adaptive control method, four chaotic complex systems are considered and the corresponding controllers are designed to realize the compound synchronization scheme. Four novel design chaotic complex systems are given as an example to verify the validity and feasibility of the proposed control scheme.
Highlights
Chaos synchronization proposed by Pecora and Carroll [1] has gained a lot of attractions for its potential application in many scientific and engineering fields in recent years
If we can realize compound synchronization scheme for three drive chaotic complex systems and one response chaotic complex system, the transmitted signals are so complex and unpredictable that they may have stronger antiattack ability and antitranslated capability than those transmitted by the traditional synchronization model
A novel chaotic complex system has been designed in this paper, whose basic dynamical properties of chaotic complex system including invariance, dissipativity, equilibria, Lyapunov exponents, bifurcation diagrams, chaotic behavior, and chaotic attractors have been discussed
Summary
Chaos synchronization proposed by Pecora and Carroll [1] has gained a lot of attractions for its potential application in many scientific and engineering fields in recent years. Compound synchronization [22, 23] have been designed to split the transmitted signals into several parts, each part loaded in different drive systems to ensure stronger antiattack ability and antitranslated capability than those transmitted by the traditional transmission model. If we can realize compound synchronization scheme for three drive chaotic complex systems and one response chaotic complex system, the transmitted signals are so complex and unpredictable that they may have stronger antiattack ability and antitranslated capability than those transmitted by the traditional synchronization model. We apply the general advantages of compound synchronization scheme [22, 23] for four real chaotic systems and extend it to four chaotic complex systems.
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