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Generic absorbing transition in coevolution dynamics

Vazquez, F.; Eguiluz, V. M.; San Miguel, M.
Physical Review Letters 100, 108702 (1-4) (2008)

We study a coevolution voter model on a network that evolves according to the state of the nodes. In a single update, a link between opposite-state nodes is rewired with probability p, while with probability 1-p one of the nodes takes its neighbor\\\'s state. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value p_c=(\\\\mu-2)/(\\\\mu-1) that only depends on the average degree \\\\mu of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as \\\\tau ~ |p_c-p|^(-1). We find that the active and frozen phases correspond to a connected and a fragmented network respectively. We show that the transition in finite-size systems can be seen as the sudden change in the trajectory of an equivalent random walk at the critical rewiring rate p_c.