Impulsive quasi-containment control in stochastic heterogeneous multiplex networks

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2024-11-05 DOI:10.1016/j.chaos.2024.115666
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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.
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随机异构多路复用网络中的脉冲准遏制控制
在这项工作中,我们提出了一个具有随机扰动的异构多路复用网络模型。我们考虑了网络中的多个领导者,并设计了一个用于节约成本的脉冲控制器,以研究随机异构多路复用网络中的遏制控制问题。通过 Lyapunov 函数方法和随机脉冲微分方程理论,我们得到了所有跟随者的状态收敛到多个领导者状态所跨的有界凸壳的充分条件。我们还得到了同步误差系统收敛区域的上界。此外,我们还研究了有时间延迟的情况,并推导出同步误差状态收敛到有界区域的充分条件。最后,我们给出了两个数值示例来验证理论结果。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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