ON THE DYNAMICS OF COMPLEX NETWORK
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Controlling complex network systems is challenging because network systems are highly coupled by ensembles and behaving with uncertainty. A network is composed by nodes and edges. Edges serve as the connection between nodes to exchange state information and further achieve state consensus. Through edges, the dynamics of individual nodes at the local level intimately affects the network dynamics at the global level. As a following bird can occasionally lose visual contact with the target bird in a flock at any moment, the edge between two nodes in a real world network systems is not necessarily always intact. Contrary to common sense, these real-world networks are usually perfectly stable even when the edges between the nodes are unstable. This suggests that not only nodes are dynamical, edges are dynamical, too. Since the edges between the nodes are changing dynamically, network configuration is also dynamical. Further, edges need be defined and quantified so that the unstable connection behavior can be properly described. The paper explores the concepts of statistical mechanics and statistical entropy to address the particular need. Statistical mechanics describes the behavior of a mechanical system that has uncertain states. Statistical entropy on the other hand defines the distribution of the microstates by probability. Entropy provides a measure of the level of network integrity. With entropy, one can assign desired dynamics to the network to ensure desired network property. This work aims to construct a complex network structure model based on the edge dynamics. Coupled with node self-dynamic and consensus law, a general dynamical network model can be constructed.
