Instability in a Network Coevolving with a Particle System

Sang-Woo Kim, Jae Dong Noh
2008 Physical Review Letters  
We study a coupled dynamics of a network and a particle system. Particles of density ρ 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 ρ_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
more » ... ensity 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.
doi:10.1103/physrevlett.100.118702 pmid:18517838 fatcat:fu5kbudsrvejxkhwih5vsyuvea