Nonlinear Dynamics

, Volume 73, Issue 3, pp 1863–1872 | Cite as

Combination synchronization of three different order nonlinear systems using active backstepping design

  • Zhaoyan Wu
  • Xinchu Fu
Original Paper


In this paper, two kinds of combination synchronization between two drive systems and one response system are investigated using active backstepping design. Firstly, increased-order combination synchronization between Lorenz system, Rössler system and hyperchaotic Lü system is considered. Secondly, reduced-order combination synchronization between hyperchaotic Lorenz system, hyperchaotic Chen system and Lü system is considered. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are both designed. Finally, several numerical examples are provided to illustrate the obtained results.


Combination synchronization Different order Chaotic Active backstepping control 



The authors would like to thank the anonymous reviewers for their very helpful suggestions and comments. This research is jointly supported by the Tianyuan Special Funds of NSFC Grant 11226242, the NSFC grant 11072136, the Natural Science Foundation of Jiangxi Province of China (20122BAB211006), the Shanghai Univ. Leading Academic Discipline Project (A.13-0101-12-004), and a grant of “The First-class Discipline of Universities in Shanghai”.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceJiangxi Normal UniversityNanchangChina
  2. 2.Department of MathematicsShanghai UniversityShanghaiChina

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