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

ABSTRACT: 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.

SUBMITTER: Gao Z

PROVIDER: S-EPMC5792007 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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

Gao Zilin Z Wang Yinhe Y

PloS one 20180131 1

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, an ...[more]

PMID: 29385183

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Project description:Network science holds great promise for expanding our understanding of the human brain in health, disease, development, and aging. Network analyses are quickly becoming the method of choice for analyzing functional MRI data. However, many technical issues have yet to be confronted in order to optimize results. One particular issue that remains controversial in functional brain network analyses is the definition of a network node. In functional brain networks a node represents some predefined collection of brain tissue, and an edge measures the functional connectivity between pairs of nodes. The characteristics of a node, chosen by the researcher, vary considerably in the literature. This manuscript reviews the current state of the art based on published manuscripts and highlights the strengths and weaknesses of three main methods for defining nodes. Voxel-wise networks are constructed by assigning a node to each, equally sized brain area (voxel). The fMRI time-series recorded from each voxel is then used to create the functional network. Anatomical methods utilize atlases to define the nodes based on brain structure. The fMRI time-series from all voxels within the anatomical area are averaged and subsequently used to generate the network. Functional activation methods rely on data from traditional fMRI activation studies, often from databases, to identify network nodes. Such methods identify the peaks or centers of mass from activation maps to determine the location of the nodes. Small (~10-20 millimeter diameter) spheres located at the coordinates of the activation foci are then applied to the data being used in the network analysis. The fMRI time-series from all voxels in the sphere are then averaged, and the resultant time series is used to generate the network. We attempt to clarify the discussion and move the study of complex brain networks forward. While the "correct" method to be used remains an open, possibly unsolvable question that deserves extensive debate and research, we argue that the best method available at the current time is the voxel-wise method.

Dataset Information

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

Publications

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

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