Combination complex synchronization of three chaotic complex systems

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• 作者：Junwei Sun (1) (2)
  Guangzhao Cui (1) (2)
  Yanfeng Wang (1) (2)
  Yi Shen (3) (4)
  
  1. College of Electric and Information Engineering ; Zhengzhou University of Light Industry ; Zhengzhou ; 450002 ; China
  2. Henan Key Lab of Information-based Electrical Appliances ; Zhengzhou University of Light Industry ; Zhengzhou ; 450002 ; China
  3. School of Automation ; Huazhong University of Science and Technology ; Hubei ; 430074 ; China
  4. Key Laboratory of Ministry of Education for Image Processing and Intelligent Control ; Huazhong University of Science and Technology ; Hubei ; 430074 ; China
  
• 关键词：Complex combination synchronization ; Complex chaotic system ; Complex scaling matrix
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：79
• 期：2
• 页码：953-965
• 全文大小：1,153 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In this paper, we firstly design a chaotic complex system and study its dynamical properties including invariance, dissipativity, equilibria, Lyapunov exponents, chaotic behavior, as well as chaotic attractors. What is more, the scaling matrices are always chosen as real matrices in previous combination synchronization schemes within two drive real systems and one response real system evolving in the same or inverse directions simultaneously. However, in many real-life applications, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, combination synchronization with regard to the complex scaling matrices, referred as combination complex synchronization, will be made the further research about three chaotic complex systems. Based on Lyapunov stability theory, three identical chaotic complex systems are considered and the corresponding controllers are designed to achieve the complex combination synchronization. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the presented control technique.