Competing edge networks

• Published in: Physics letters. A Vol. 376; no. 32; pp. 2167 - 2173
• Main Authors: Parsons, Mark, Grindrod, Peter
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 25.06.2012
• Subjects: Bifurcation structure; Communication networks; Competition; Displacement; Edgewise competition; Evolving networks; Mathematical analysis; Mathematical models; Mean field approximation; Networks; Nonlinearity; Solid state physics; Mean field approximation; Bifurcation structure; Edgewise competition; Evolving networks
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2012.05.008

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 otherʼs growth and encourage the otherʼs 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. ► A model for edgewise-competing evolving network pairs is introduced. ► Defined competition equations yield to a mean field analysis. ► Multiple equilibrium states and different bifurcation types can occur. ► The system is sensitive to sparse initial conditions and near unstable equilibriums.