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Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control

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Abstract

This paper investigates the issue of almost sure cluster synchronization in nonlinearly coupled complex networks with nonidentical nodes and time-varying delay. These networks are modulated by a continuous-time Markov chain and disturbed by a Brownian movement. The decentralized adaptive update law and pinning control protocol are employed in designing controllers for guaranteeing almost sure cluster synchronization. By constructing a novel stochastic Lyapunov–Krasovskii function and using the stochastic Lasalle-type invariance theorem, some sufficient conditions for almost sure cluster synchronization of the networks are derived. Finally, a numerical example is given to testify the effectiveness of the theoretical results.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (11001179, 61273220, 61373087). The authors are very grateful to reviewers and editors for their valuable comments and suggestions to improve the presentation of the paper.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Hailing Dong, Danfeng Ye & Jianwen Feng

  2. Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Optoelectronic Engineering, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Jingyi Wang

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  1. Hailing Dong
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  2. Danfeng Ye
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  3. Jianwen Feng
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  4. Jingyi Wang
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Correspondence to Hailing Dong.

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Dong, H., Ye, D., Feng, J. et al. Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control. Nonlinear Dyn 87, 727–739 (2017). https://doi.org/10.1007/s11071-016-3071-z

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  • DOI: https://doi.org/10.1007/s11071-016-3071-z

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