复杂网络中活性-非活性聚类的对称诱导活动模式
Symmetry-induced activity patterns of active-inactive clusters in complex networks
AI总结：
研究通过网络结构的对称性与动态设计，揭示了复杂网络中活性与非活性聚类共存的稳定模式，分析了耦合变化对活动模式转换的影响。
摘要：
同步模式表征网络中节点根据同步动态形成聚类的状态。同步聚类可能表现出活性或非活性状态。活性和非活性聚类的同时不变性对动态系统施加了约束，因为来自活性聚类的波动必须相互抵消以使目标聚类保持非活性。通过利用网络结构中的排列对称性，并在结构上选择动态，使得内部动态和耦合函数在相空间中为奇函数，我们证明这种结构和动态的组合会产生由共存的活性和非活性聚类组成的稳定不变模式。网络中的对称性生成与自身反同步的活性聚类，导致与这些反同步聚类连接的聚类波动抵消。我们使用全网络对称性获得同步聚类，而商网络对称性用于寻找共存的活性-非活性状态。我们显示，随着节点间耦合的变化，活性聚类在不同耦合值处失去活性，网络从一种活动模式过渡到另一种。对Van der Pol和Stuart-Landau振荡器网络进行了数值模拟。最后，我们将主稳定性框架扩展到这些模式，并为它们的存在提供了稳定性条件。
英文摘要：
Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active and inactive clusters of synchronized nodes poses a dynamical constraint because fluctuations from active clusters must cancel out for a desired cluster to be inactive. By exploiting permutation symmetries in the network structure and choosing dynamics on top such that internal dynamics and coupling functions are odd functions in the phase space, we demonstrate that this combination of structure and dynamics exhibits stable invariant patterns composed of coexisting active and inactive clusters. The symmetries in a network generate active clusters that are in antisynchrony with each other, resulting in the cancellation of fluctuations for clusters connected with these antisynchronous clusters. We use full network symmetries to obtain synchronized clusters, while quotient network symmetries are used to find coexisting active-inactive states of clusters. We show that as the coupling between nodes changes, active clusters lose their activity at different coupling values, and the network transitions from one activity pattern to another. Numerical simulations are presented for networks of Van der Pol and Stuart-Landau oscillators. Finally, we extend the master stability framework to these patterns and provide stability conditions for their existence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
