Instability in a Network Coevolving with a Particle System

Abstract

We study the coupled dynamics of a network and a particle system. Particles of density rho diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics leads to an instability toward the formation of hubs and that there is a dynamic phase transition at a threshold particle density rho c. In the low density phase, the network evolves into a star-shaped one with the maximum degree growing linearly in time. In the high density phase, the network exhibits a fat-tailed degree distribution and an interesting dynamic scaling behavior. We present an analytic theory explaining the mechanism for the instability and a scaling theory for the dynamic scaling behavior.