Competing edge networks

Journal article

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 others growth and encourage the others 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. © 2012 Elsevier B.V.

Authors: Parsons, M; Grindrod, P

• Journal: Physics Letters, Section A: General, Atomic and Solid State Physics
• Volume: 376
• Issue: 32
• Pages: 2167-2173
• Publication date: 2012-06-25
• DOI: 10.1016/j.physleta.2012.05.008
• ISSN: 0375-9601
• Language: English
• Keywords: Mean field approximation; Bifurcation structure; Edgewise competition; Evolving networks