Cluster synchronization of Markovian switching complex networks with hybrid couplings and stochastic perturbations

Quan Liu, Bao Kan, Qiang Wang and Yilin Fang

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: In this work, we extend cluster synchronization into a more general complex network model, a class of Markovian switching complex networks composed of nonidentical nodes with hybrid couplings. These networks are also influenced by coupling delays and disturbed by stochastic noise perturbations. Based on some definitions, assumptions and lemmas, an adaptive controller is designed. Particularly, by constructing a novel stochastic Lyapunov–Krasovskii function and employing the linear matrix inequalities (LMIs), Ito’s formula and the stochastic Lasalle-type invariance theorem, the effectiveness of the designed controller is proved. Besides, a numerical example is illustrated for further verifications and conclusions.

Keywords: Cluster synchronization; Markovian switching; Hybrid coupling; Coupling delay; Stochastic noise perturbation; Adaptive control (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119305618

DOI: 10.1016/j.physa.2019.04.173

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