{"title":"On synchronization of random nonlinear complex networks","authors":"Zhicheng Zhang , Yan Zhang , Yingxue Du","doi":"10.1016/j.physd.2024.134396","DOIUrl":null,"url":null,"abstract":"<div><div>Traditionally, stochastic disturbances arising in complex networks are often assumed to be drawn from a Wiener process, potentially limiting their applicability in real engineering scenarios. To address this limitation, we incorporate randomness to quantify the stochastic disturbances within a group of participating individuals, thereby establishing random nonlinear complex networks in a directed interacting setting. Subsequently, we demonstrate that the maximal existence interval of the unique solution to the underlying systems is determined by the properties of the associated noise and the specified Lipschitz constant. Building on this, we further show that, by making use of supermartingale and Lyapunov-based techniques, the almost sure synchronization condition of the investigated random complex system is determined by the communication topology, weight gain, and the number of participating agents. Additionally, we discuss synchronization problems within strongly connected and undirected graphs. Finally, we validate the proposed method using Chen systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134396"},"PeriodicalIF":2.7000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003464","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Traditionally, stochastic disturbances arising in complex networks are often assumed to be drawn from a Wiener process, potentially limiting their applicability in real engineering scenarios. To address this limitation, we incorporate randomness to quantify the stochastic disturbances within a group of participating individuals, thereby establishing random nonlinear complex networks in a directed interacting setting. Subsequently, we demonstrate that the maximal existence interval of the unique solution to the underlying systems is determined by the properties of the associated noise and the specified Lipschitz constant. Building on this, we further show that, by making use of supermartingale and Lyapunov-based techniques, the almost sure synchronization condition of the investigated random complex system is determined by the communication topology, weight gain, and the number of participating agents. Additionally, we discuss synchronization problems within strongly connected and undirected graphs. Finally, we validate the proposed method using Chen systems.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.