Fragmentation transitions in a coevolving nonlinear voter model.
Fragmentation transitions in a coevolving nonlinear voter model.
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DOI：
10.1038/s41598-017-13047-2
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发表时间：
2017-10-09
影响因子：
4.6
通讯作者：
Miguel MS
中科院分区：
文献类型：
--
作者：
Min B;Miguel MS
我们研究了一个描述节点状态和网络拓扑耦合演化的协同演化非线性选举模型。相互作用的非线性通过参数q来衡量。通过解析和数值分析，我们得到了一个相图在p，q参数空间中有三个不同的阶段：动态活跃的共存阶段在一个单一的组件网络，吸收共识阶段在一个单一的组件网络，吸收阶段在一个碎片化的网络。对于有限系统的活动阶段有一个寿命，系统的大小呈指数增长，在方差与线性选民模型，具有一个生命周期成比例的系统大小的类似阶段。我们发现三个过渡线，满足线性选民模型的碎片过渡点。第一过渡线对应于活性相和破碎相之间的连续吸收过渡。另外两条过渡线是不连续的过渡，与线性选民模型的过渡有根本的不同。一种是一致性阶段和碎片化阶段之间的碎片化过渡，另一种是活跃阶段和一致性阶段之间的单组分网络中的吸收过渡。
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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