Instability in a Network Coevolving with a Particle System

Abstract

We study a 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 mechanism for the instability and a scaling theory for the dynamic scaling behavior.

4 pages and 5 figures

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• Particle Condensation in Pair Exclusion Process
• Structural phase transition in evolving networks
• Moment-Closure Approximations for Discrete Adaptive Networks
• Spatially self-organized resilient networks by a distributed cooperative mechanism
• Self-organized network design by link survivals and shortcuts
• Condensation and Clustering in the Driven Pair Exclusion Process