Fragmentation transitions in a coevolving nonlinear voter model

TL;DR

This paper investigates a coevolving nonlinear voter model, revealing a complex phase diagram with active, consensus, and fragmented phases, and identifies both continuous and discontinuous transitions influenced by nonlinearity and rewiring.

Contribution

It introduces a detailed phase diagram for the nonlinear voter model with coevolving networks, highlighting novel discontinuous transitions and the impact of nonlinearity on network fragmentation.

Findings

Identifies three distinct phases: active, consensus, and fragmented.

Discovers both continuous and discontinuous phase transitions.

Shows active phase lifetime grows exponentially with system size.

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.