复杂网络中自适应耦合诱导的多稳态
Adaptive coupling induced multi-stable states in complex networks
摘要：
自适应耦合是控制复杂网络动态特性和简化复杂网络中各种过程的关键因素之一，其中耦合是动态的，并且依赖于复杂系统中振子的行为。在本文中，我们已经证明了多稳态的发生在一个系统的同相振荡器的动态耦合。我们发现，多稳态是由两个集群的同步状态，其中集群是在彼此的反相关系和去同步化状态。我们还发现，无论系统中是否存在同步或去同步，振子之间的相位关系都是渐近稳定的。耦合的时间尺度影响两团簇状态下团簇的大小。我们还研究了耦合不对称性和塑性不对称性对多稳态的影响。在没有耦合不对称的情况下，增加塑性不对称性会导致系统从两个聚集状态到去聚集状态，然后到两个聚集状态。此外，耦合不对称性（如果存在的话）也影响该转变。我们还解析地发现了上述多稳态-去极化-多稳态转变的发生。对非全同振子的相位演化也作了简要的讨论。我们的分析结果与我们的数值观测是一致的。
英文摘要：
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this paper, we have demonstrated the occurrence of multi-stable states in a system of identical phase oscillators that are dynamically coupled. We find that the multi-stable state is comprised of a two cluster synchronization state where the clusters are in anti-phase relationship with each other and a desynchronization state. We also find that the phase relationship between the oscillators is asymptotically stable irrespective of whether there is synchronization or desynchronization in the system. The time scale of the coupling affects the size of the clusters in the two cluster state. We also investigate the effect of both the coupling asymmetry and plasticity asymmetry on the multi-stable states. In the absence of coupling asymmetry, increasing the plasticity asymmetry causes the system to go from a two clustered state to a desynchronization state and then to a two clustered state. Further, the coupling asymmetry, if present, also affects this transition. We also analytically find the occurrence of the above mentioned multi-stable-desynchronization-multi-stable state transition. A brief discussion on the phase evolution of nonidentical oscillators is also provided. Our analytical results are in good agreement with our numerical observations.
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。
