Competing edge networks |
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Authors: | Mark Parsons Peter Grindrod |
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Institution: | School of Mathematics and Physical Sciences, University of Reading, Whiteknights, PO Box 220, Reading, RG6 6AX, United Kingdom |
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Abstract: | We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the other?s growth and encourage the other?s demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails. |
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Keywords: | Evolving networks Edgewise competition Mean field approximation Bifurcation structure |
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