{"title":"具有任意耦合的有向多层复杂网络的同步与控制","authors":"Leijing Xie, Xiwei Liu","doi":"10.1002/rnc.8065","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this article, we focus on the synchronization problem of directed multilevel complex networks (MLevelN) with arbitrary couplings. First, we propose a new MLevelN model with arbitrarily connected couplings, thus previous fully or partially one-to-one connected couplings can be regarded as special cases for this model. Then, using the normalized left eigenvector of couplings, criteria on two typical types of synchronization for MLevelN are obtained. Besides, we consider MLevelN with disconnected layers, and by using Tarjan's algorithm, it can be rearranged to MLevelN with different number of nodes in different layers. Furthermore, different control strategies for the rearranged MLevelN are also designed, and pinning only one node (arbitrarily chosen) can make the whole MLevelN realize complete synchronization. Then, the results are applied on a three-level reaction-diffusion neural network as an application. Finally, the effectiveness of the obtained criteria is verified by numerical simulations.</p>\n </div>","PeriodicalId":50291,"journal":{"name":"International Journal of Robust and Nonlinear Control","volume":"35 15","pages":"6338-6358"},"PeriodicalIF":3.2000,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Synchronization and Control for Directed Multilevel Complex Networks With Arbitrary Couplings\",\"authors\":\"Leijing Xie, Xiwei Liu\",\"doi\":\"10.1002/rnc.8065\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In this article, we focus on the synchronization problem of directed multilevel complex networks (MLevelN) with arbitrary couplings. First, we propose a new MLevelN model with arbitrarily connected couplings, thus previous fully or partially one-to-one connected couplings can be regarded as special cases for this model. Then, using the normalized left eigenvector of couplings, criteria on two typical types of synchronization for MLevelN are obtained. Besides, we consider MLevelN with disconnected layers, and by using Tarjan's algorithm, it can be rearranged to MLevelN with different number of nodes in different layers. Furthermore, different control strategies for the rearranged MLevelN are also designed, and pinning only one node (arbitrarily chosen) can make the whole MLevelN realize complete synchronization. Then, the results are applied on a three-level reaction-diffusion neural network as an application. Finally, the effectiveness of the obtained criteria is verified by numerical simulations.</p>\\n </div>\",\"PeriodicalId\":50291,\"journal\":{\"name\":\"International Journal of Robust and Nonlinear Control\",\"volume\":\"35 15\",\"pages\":\"6338-6358\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2025-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Robust and Nonlinear Control\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/rnc.8065\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Robust and Nonlinear Control","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/rnc.8065","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Synchronization and Control for Directed Multilevel Complex Networks With Arbitrary Couplings
In this article, we focus on the synchronization problem of directed multilevel complex networks (MLevelN) with arbitrary couplings. First, we propose a new MLevelN model with arbitrarily connected couplings, thus previous fully or partially one-to-one connected couplings can be regarded as special cases for this model. Then, using the normalized left eigenvector of couplings, criteria on two typical types of synchronization for MLevelN are obtained. Besides, we consider MLevelN with disconnected layers, and by using Tarjan's algorithm, it can be rearranged to MLevelN with different number of nodes in different layers. Furthermore, different control strategies for the rearranged MLevelN are also designed, and pinning only one node (arbitrarily chosen) can make the whole MLevelN realize complete synchronization. Then, the results are applied on a three-level reaction-diffusion neural network as an application. Finally, the effectiveness of the obtained criteria is verified by numerical simulations.
期刊介绍：
Papers that do not include an element of robust or nonlinear control and estimation theory will not be considered by the journal, and all papers will be expected to include significant novel content. The focus of the journal is on model based control design approaches rather than heuristic or rule based methods. Papers on neural networks will have to be of exceptional novelty to be considered for the journal.
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