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

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...

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Bibliographic Details
Published inNonlinear dynamics Vol. 87; no. 2; pp. 727 - 739
Main Authors Dong, Hailing, Ye, Danfeng, Feng, Jianwen, Wang, Jingyi
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2017
Springer Nature B.V
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Summary: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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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-3071-z