Fragmentation transitions in a coevolving nonlinear voter model

Abstract

We study a coevolving nonlinear voter model describing the coupled evolution of the states of the nodes and the network topology. Nonlinearity of the interaction is measured by a parameter q. The network topology changes by rewiring links at a rate p. By analytical and numerical analysis we obtain a phase diagram in p, q parameter space with three different phases: Dynamically active coexistence phase in a single component network, absorbing consensus phase in a single component network, and absorbing phase in a fragmented network. For finite systems the active phase has a lifetime that grows exponentially with system size, at variance with the similar phase for the linear voter model that has a lifetime proportional to system size. We find three transition lines that meet at the point of the fragmentation transition of the linear voter model. A first transition line corresponds to a continuous absorbing transition between the active and fragmented phases. The other two transition lines are discontinuous transitions fundamentally different from the transition of the linear voter model. One is a fragmentation transition between the consensus and fragmented phases, and the other is an absorbing transition in a single component network between the active and consensus phases.

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References in corpus (9)

• Adaptive Coevolutionary Networks: A Review
• Co-evolution of strategy and structure in complex networks with dynamical linking
• Nonequilibrium phase transition in the coevolution of networks and opinions
• Homophily, Cultural Drift and the Co-Evolution of Cultural Groups
• Generic Absorbing Transition in Coevolution Dynamics
• Making new connections towards cooperation in the prisoner's dilemma game
• Self-organization towards optimally interdependent networks by means of coevolution
• Analytical Solution of the Voter Model on Disordered Networks
• Absorbing and Shattered Fragmentation Transitions in Multilayer Coevolution