Competing edge networks
Parsons, M. C. and Grindrod, P. (2012) Competing edge networks. Physics Letters A. ISSN 0375-9601 (In Press)
To link to this article 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, sub ject 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 nonlin- ear 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 peer-to-peer communication net- works such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails.