Diakonova Marina, San Miguel Maxi, Eguíluz Víctor M
Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062818. doi: 10.1103/PhysRevE.89.062818. Epub 2014 Jun 30.
We introduce a coevolution voter model in a multilayer by coupling a fraction of nodes across two network layers (the degree of multiplexing) and allowing each layer to evolve according to its own topological temporal scale. When these time scales are the same, the time evolution equations can be mapped to a coevolution voter model in a single layer with an effective average degree. Thus the dynamics preserve the absorbing-fragmentation transition at a critical value that increases with the degree of multiplexing. When the two layers have different topological time scales, we find an anomalous transition, named shattered fragmentation, in which the network in one layer splits into two large components in opposite states and a multiplicity of isolated nodes. We identify the growth of the number of components as a signature of this anomalous transition. We also find the critical level of interlayer coupling needed to prevent the fragmentation in a layer connected to a layer that does not fragment.
我们通过在两个网络层之间耦合一部分节点（复用程度）并允许每层根据其自身的拓扑时间尺度演化，引入了一种多层协同进化选民模型。当这些时间尺度相同时，时间演化方程可以映射到具有有效平均度的单层协同进化选民模型。因此，动力学在一个随复用程度增加的临界值处保持吸收 - 碎片化转变。当两层具有不同的拓扑时间尺度时，我们发现了一种异常转变，称为破碎碎片化，其中一层中的网络分裂成处于相反状态的两个大组件以及多个孤立节点。我们将组件数量的增长确定为这种异常转变的一个特征。我们还找到了防止与未碎片化层相连的层发生碎片化所需的层间耦合临界水平。
