Impulsive quasi-containment control in stochastic heterogeneous multiplex networks

Xin Jin, Zhengxin Wang and Xiaojie Chen

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: In this work, we propose a model for heterogeneous multiplex networks with stochastic perturbations. We consider multiple leaders in the networks and design an impulsive controller for cost saving to investigate the containment control problem in the stochastic heterogeneous multiplex networks. By means of the Lyapunov function method and stochastic impulsive differential equations theory, we obtain sufficient conditions in which the states of all followers converge to the bounded convex hull spanned by the states of multiple leaders. We also obtain the upper bound of the convergence region of the synchronization error system. Furthermore, we study the case with time delay and derive the sufficient conditions for the states of synchronization error to converge to the bounded region. Finally, we give two numerical examples to verify the theoretical results.

Keywords: Heterogeneous multiplex networks; Quasi-containment control; Stochastic perturbations; Impulsive control; Time delay (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012189

DOI: 10.1016/j.chaos.2024.115666

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