Presentacion oral: Absorbing Phase Transition in Coevolving Networks

FEDERICO VAZQUEZ

Creta

Conferencia; Sigmaphi-2008 International Conference; 2008

Since the investigation of networks by statistical physicists began, theresearch has been focus in many aspects.  One of this is related to the studyof different dynamical processes on networks, such as epidemic spreading inbiology, reaction-diffusion in chemistry, opinion formation in sociology, etc.Most of these studies assume that the network of interactions is fixed.However, in many real cases, the topology of the network is affected by thestate of the nodes  and vice versa, so that the network adapts to the process.In recent  studies on adaptive networks  people have observed a peculiar typeof  absorbing phase transition.  Inthese models, a node can change its state by interacting with its neighbors,and at the same time, links can be rewired depending on the state of the nodesat their ends.  In this way, the dynamics of nodes and links are notindependent, but they coevolve.  It is found that when the rewiring is fastenough compare to the rate at which nodes update their states, the networkbreaks into disconnected components, each composed by nodes holding the samestate.  In order to understand the mechanism of this fragmentation transitionI introduce a simple model, that  possesses all theingredients of related models, and has the advantage of being analyticallytractable.  A mean-field approximation reveals an absorbing transition from anactive to a frozen phase at a critical value of the rewiring probabilityp_c=(mu-2)/(mu-1) that only depends on the average degree mu of thenetwork.  In finite-size systems, the active and frozen phases correspond to aconnected  and a fragmented network respectively.  The transition can be seenas the sudden change in the trajectory  of an equivalent random walk at thecritical point, resulting in an approach to  the final frozen state whose timescale diverges as tau ~ |p_c-p|^-1  near p_c.  The mean-fieldapproach can be extended to study the time evolution of the system in genericinteracting agents models on complex networks.