Nonlinear Dynamics

, Volume 73, Issue 3, pp 1211–1222 | Cite as

Combination–combination synchronization among four identical or different chaotic systems

  • Junwei Sun
  • Yi ShenEmail author
  • Guodong Zhang
  • Chengjie Xu
  • Guangzhao Cui
Original Paper


Based on one drive system and one response system synchronization model, a new type of combination–combination synchronization is proposed for four identical or different chaotic systems. According to the Lyapunov stability theorem and adaptive control, numerical simulations for four identical or different chaotic systems with different initial conditions are discussed to show the effectiveness of the proposed method. Synchronization about combination of two drive systems and combination of two response systems is the main contribution of this paper, which can be extended to three or more chaotic systems. A universal combination of drive systems and response systems model and a universal adaptive controller may be designed to our intelligent application by our synchronization design.


Combination–combination synchronization Lorenz system Rössler system Chen’s system Lü system 



The authors thank the editor and the anonymous reviewers for their resourceful and valuable comments and constructive suggestions. The work is supported the State Key Program of National Natural Science of China (Grant No. 61134012), the National Science Foundation of China (Grant Nos. 60970084, 61070238), Basic and Frontier Technology Research Program of Henan Province (Grant No. 122300413211), the Distinguished Talents Program of Henan Province (Grant No. 124200510017), China Postdoctoral Science Foundation funded project under Grant 2012M511615.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Junwei Sun
    • 1
    • 2
    • 3
  • Yi Shen
    • 1
    • 2
    Email author
  • Guodong Zhang
    • 1
    • 2
  • Chengjie Xu
    • 1
    • 2
  • Guangzhao Cui
    • 3
  1. 1.Department of Control Science and EngineeringHuazhong University of Science and TechnologyHubeiChina
  2. 2.Key Laboratory of Ministry of Education for Image Processing and Intelligent ControlHuazhong University of Science and TechnologyHubeiChina
  3. 3.Henan Key Lab of Information-based Electrical AppliancesZhengzhou University of Light IndustryZhengzhouChina

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