The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings

The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which...

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Autores principales: Gao, Zilin, Wang, Yinhe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5792007/
https://www.ncbi.nlm.nih.gov/pubmed/29385183
http://dx.doi.org/10.1371/journal.pone.0191941
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author Gao, Zilin
Wang, Yinhe
author_facet Gao, Zilin
Wang, Yinhe
author_sort Gao, Zilin
collection PubMed
description The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which are mainly caused by coupling effect of connection relationships between nodes. However, the connection relationships between nodes are also one main body of a time-varying dynamic complex network, and thus they may evolve with time and maybe show certain characteristic phenomena. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. Therefore, it is important to investigate theoretically the reasons in dynamics for the occurrence. Especially, from the angle of large-scale systems, how the dynamic behaviors of nodes (such as the individuals, neurons) contribute to the connection relationships is one of worthy research directions. In this paper, according to the structural balance theory of triad proposed by F. Heider, we mainly focus on the connection relationships body, which is regarded as one of the two subsystems (another is the nodes body), and try to find the dynamic mechanism of the structural balance with the internal state behaviors of the nodes. By using the Riccati linear matrix differential equation as the dynamic model of connection relationships subsystem, it is proved under some mathematic conditions that the connection relationships subsystem is asymptotical structural balance via the effects of the coupling roles with the internal state of nodes. Finally, the simulation example is given to show the validity of the method in this paper.
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spelling pubmed-57920072018-02-09 The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings Gao, Zilin Wang, Yinhe PLoS One Research Article The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which are mainly caused by coupling effect of connection relationships between nodes. However, the connection relationships between nodes are also one main body of a time-varying dynamic complex network, and thus they may evolve with time and maybe show certain characteristic phenomena. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. Therefore, it is important to investigate theoretically the reasons in dynamics for the occurrence. Especially, from the angle of large-scale systems, how the dynamic behaviors of nodes (such as the individuals, neurons) contribute to the connection relationships is one of worthy research directions. In this paper, according to the structural balance theory of triad proposed by F. Heider, we mainly focus on the connection relationships body, which is regarded as one of the two subsystems (another is the nodes body), and try to find the dynamic mechanism of the structural balance with the internal state behaviors of the nodes. By using the Riccati linear matrix differential equation as the dynamic model of connection relationships subsystem, it is proved under some mathematic conditions that the connection relationships subsystem is asymptotical structural balance via the effects of the coupling roles with the internal state of nodes. Finally, the simulation example is given to show the validity of the method in this paper. Public Library of Science 2018-01-31 /pmc/articles/PMC5792007/ /pubmed/29385183 http://dx.doi.org/10.1371/journal.pone.0191941 Text en © 2018 Gao, Wang http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Gao, Zilin
Wang, Yinhe
The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title_full The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title_fullStr The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title_full_unstemmed The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title_short The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
title_sort structural balance analysis of complex dynamical networks based on nodes' dynamical couplings
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5792007/
https://www.ncbi.nlm.nih.gov/pubmed/29385183
http://dx.doi.org/10.1371/journal.pone.0191941
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