自适应网络系统中动力群的自发形成
Spontaneous Formation of Dynamical Groups in an Adaptive Networked System
摘要：
在这项工作中，我们研究了一个自适应网络动力系统的模型，其中的相位振荡器之间的耦合强度与相态共同演化。结果表明，在该模型中，振子经过长时间的演化，可以自发地分化为两个动力学群。在每个组内，振荡器具有相似的相位，而不同组中的振荡器具有近似相反的相位。该网络由最初的连接强度均匀分布的随机结构逐渐转变为内部连接强、内部连接弱的模块化结构。此外，连接强度遵循幂律分布，这是网络和动力学共同进化的自然结果。有趣的是，我们发现，如果相互联系弱于某个阈值，这两个动力学群将几乎解耦和独立发展。这些结果有助于进一步理解许多社会和生物网络中的经验观察。
英文摘要：
In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into two dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure which is characterized by strong intra connections and weak inter connections. Furthermore, the connection strengths follow a power law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks.
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