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Time scale competition leading to fragmentation and recombination transitions in the co-evolution of network and states.

Vazquez, Federico; Gonzalez-Avella,Juan Carlos; Eguiluz, Victor M.;San Miguel, Maxi.
Physical Review E 76, 046120 (1-5) (2007)

We study the coevolution of network structure and node states in a model of multiple state interacting agents. The system displays two transitions, network recombination and fragmentation, governed by time scales that emerge from the dynamics. The recombination transition separates a frozen configuration, composed by disconnected network components whose agents share the same state, from an active configuration, with a fraction of links that are continuously being rewired. The nature of this transition is explained analytically as the maximum of a characteristic time. The fragmentation transition, that appears between two absorbing frozen phases, is an anomalous order-disorder transition, governed by a crossover between the time scales that control the structure and state dynamics.