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Pinning cluster synchronization of delayed complex dynamical networks with nonidentical nodes and impulsive effects

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Abstract

This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive control approach is proposed to achieve the exponential cluster synchronization of the considered network. By employing a time-dependent Lyapunov functional, less conservative cluster synchronization criteria are established in the form of linear matrix inequalities. Compared with the existing works, the constructed Lyapunov functional is related with impulse time sequence, which makes full use of the information on dynamical characteristic of synchronization error dynamics. Finally, a numerical example of typical chua’s system is given to illustrate the effectiveness and correctness of the theoretical results.

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Acknowledgements

The authors are grateful to the reviewers and editors for their valuable comments and suggestions to improve the presentation of this paper. This work is supported by the National Natural Science Foundation of China (Nos. 61273015 and 61533006), China Scholarship Council (CSC), Key project of Natural Science Research of Anhui Provincial Department of Education and NSERC Canada.

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Authors and Affiliations

  1. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Xin Wang & Kun She

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Shouming Zhong & Huilan Yang

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  1. Xin Wang
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  2. Kun She
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  3. Shouming Zhong
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  4. Huilan Yang
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Correspondence to Xin Wang.

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Wang, X., She, K., Zhong, S. et al. Pinning cluster synchronization of delayed complex dynamical networks with nonidentical nodes and impulsive effects. Nonlinear Dyn 88, 2771–2782 (2017). https://doi.org/10.1007/s11071-017-3410-8

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  • DOI: https://doi.org/10.1007/s11071-017-3410-8

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