Presentacion oral: Absorbing Phase Transition in Coevolving Networks

FEDERICO VAZQUEZ

Palma de Mallorca

Workshop; Workshop on Dynamics and Evolution of Biological and Social Networks; 2008

I will talk about a particular type of absorbing transitions that has recentlybeen observed in models of adaptive networks.  In these models, a node canchange its state by interacting with its neighbors, and at the same time,links can be rewired depending on the state of the nodes at their ends.  Inthis way, the dynamics of nodes and links are not independent, but theycoevolve.  It is found that when the rewiring is fast enough compare to therate at which nodes update their states, the network breaks into disconnectedcomponents, each composed by nodes holding the same state.  In order tounderstand the mechanism of this fragmentation transition I will introduce asimple model, that possesses all the ingredients of related models, and hasthe advantage of being analytically tractable.  A mean-field approximationreveals an absorbing transition from an active to a frozen phase at a criticalvalue of the rewiring probability p_c=(mu-2)/(mu-1) that only dependson the average degree mu of the network.  In finite-size systems, theactive and frozen phases correspond to a connected  and a fragmented networkrespectively.  The transition can be seen as the sudden change in thetrajectory  of an equivalent random walk at the critical point, resulting inan approach to  the final frozen state whose time scale diverges as tau ~|p_c-p|^-1  near p_c.