Nonlinear Dynamics

, Volume 70, Issue 2, pp 1107–1115 | Cite as

Cluster synchronization analysis of complex dynamical networks by input-to-state stability

  • Junchan ZhaoEmail author
  • M. A. Aziz-Alaoui
  • Cyrille Bertelle
Original Paper


Cluster synchronization is an interesting issue in complex dynamical networks with community structure. In this paper, we study cluster synchronization of complex networks with non-identical systems by input-to-state stability. Some sufficient conditions that ensure cluster synchronization of complex networks are provided. We show that the cluster synchronization is difficult to achieve if there are some links among different clusters. The analysis is then extended to the case where the outer coupling strengths are adaptive. Finally, numerical simulations are given to validate our theoretical analysis.


Complex network Cluster synchronization Input-to-state stability Adaptive control 



This work was jointly supported by Région Haute-Normandie France and FEDER-RISC, the National Natural Science Foundation of China under Grant Nos. 11172215, 11071280, 50739003, the Youth Project of Hubei Education Department under Grant Nos. Q20111607, Q20111611, and the Foundation of Wuhan Textile University under Grant No. 113073. The authors wish to thank the reviewers and editor for their valuable comments and suggestions.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Junchan Zhao
    • 1
    • 2
    Email author
  • M. A. Aziz-Alaoui
    • 2
  • Cyrille Bertelle
    • 3
  1. 1.College of Mathematica and Computer ScienceWuhan Textile UniversityWuhanChina
  2. 2.Applied Mathematics LaboratoryUniversity of Le HavreLe Havre CedexFrance
  3. 3.LITISUniversity of Le HavreLe Havre CedexFrance

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