网络拓扑与动力学的一般协同演化
General coevolution of topology and dynamics in networks
摘要：
我们提出了一个一般的框架，在动力系统的共同进化的研究。这种现象是由两个相互作用的网络元素的动力学过程的共存：节点状态的变化和重新布线的节点之间的链接。重新布线的过程是根据两个基本动作来描述的：节点之间的断开连接和重新连接，两者都基于它们的状态比较机制。我们假设重新布线和节点状态改变的过程分别以概率Pr和Pc发生，彼此独立。协同进化系统的集体行为可以在参数空间（Pr，Pc）上刻画。作为一个应用，对于一个类似投票者的节点动力学，我们发现具有相似状态的节点之间的重新连接会导致网络分裂。在此空间上计算了具有不同性质的网络发生碎裂的临界边界。我们表明，协同进化模型对应于曲线在这个空间上描述的功能之间的关系Pr和Pc。一个大的域阶段和一个破碎的阶段在网络中的发生预测不同的模型，并发现与一些早期的结果协议。系统的集体行为也在断开和重接行为的参数空间上得到了刻画。在这个空间的一个区域中，我们发现了一种行为，在这种行为中，不同的节点状态可以在一个大型的连接网络上共存很长时间。
英文摘要：
We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes. The process of rewiring is described in terms of two basic actions: disconnection and reconnection between nodes, both based on a mechanism of comparison of their states. We assume that the process of rewiring and node state change occur with probabilities Pr and Pc respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (Pr, Pc). As an application, for a voterlike node dynamics we find that reconnections between nodes with similar states lead to network fragmentation. The critical boundaries for the onset of fragmentation in networks with different properties are calculated on this space. We show that coevolution models correspond to curves on this space describing functional relations between Pr and Pc. The occurrence of a one-large-domain phase and a fragmented phase in the network is predicted for diverse models, and agreement is found with some earlier results. The collective behavior of system is also characterized on the space of parameters for the disconnection and reconnection actions. In a region of this space, we find a behavior where different node states can coexist for very long times on one large, connected network.
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