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An almost-solvable model of complex network dynamics. (English) Zbl 1462.90028

Summary: We discuss a specific model, which we refer to as RandLOE, of a large multi-agent network whose dynamic is prescribed via a combination of deterministic local laws and random exogenous factors. The RandLOE approach lies outside the framework of Stochastic Differential Equations, but lends itself to analytic examination as well as to stable simulation even for relatively large networks. RandLOE is based on the logistic operator equation (LOE), which is a multidimensional dynamical system extending the classical logistic equation via an operator-algebraic interaction term. The network is defined by interpreting the LOE variable as an adjacency matrix of a complete graph. Depending on the choice of parameters, it can display a number of essentially distinct dynamical characteristics: e.g., cycles of expansion and contraction.
Editorial remark: References to figures are missing (only given as ??, likely due to incomplete compiling).

MSC:

90B10 Deterministic network models in operations research
05C82 Small world graphs, complex networks (graph-theoretic aspects)
68M10 Network design and communication in computer systems

Software:

Cytoscape; Python
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Full Text: DOI arXiv

References:

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