Generic absorbing transition in coevolution dynamics

We study a coevolution voter model on a complex network. 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. In finite-size systems, the active and frozen phases correspond to a connected and a fragmented network, respectively. The transition can be seen as the sudden change in the trajectory of an equivalent random walk at the critical point, resulting in an approach to the final frozen state whose time scale diverges as tau similar to |p(c) - p|(-1) near p(c).