标题： 不可同步的复杂网络中的非平稳模式 显示英文标题

标题： Nonstationary pattern in unsynchronizable complex networks

摘要： 在不可同步的复杂网络中，模式形成和演化被研究。 由于拓扑的不对称性，复杂网络中形成的同步模式是不规则且非平稳的。 对于耦合强度刚刚超出可同步区域的情况，系统动力学的典型现象是开-关间歇性。 在此过程中出现的模式由一个包含大多数节点的巨大簇和少量小簇共存所标志。 模式演化的特点是巨大簇不规则地吸收或释放小簇。 随着耦合强度远离同步分岔点，巨大簇逐渐分解为多个小簇，系统动力学表现为小簇的整合与分离。 对非平稳模式演化的动态机制和统计特性进行了分析和研究，并揭示了一些新的标度关系。 值得注意的是，发现那些以高频率逃离巨大簇的少数活跃节点，与耦合强度无关，但对分岔类型敏感。 我们希望关于非平稳模式的研究结果能为复杂系统的动力学提供额外的理解，并对一些只有在不可同步状态下才能维持正常功能的实际问题具有启示意义。 显示英文摘要

摘要： Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately out of the synchronizable region, the typical phenomenon is the on-off intermittency of the system dynamics. The patterns appeared in this process are signatured by the coexistence of a giant cluster, which comprises most of the nodes, and a few number of small clusters. The pattern evolution is characterized by the giant cluster irregularly absorbs or emits the small clusters. As the coupling strength leaves away from the synchronization bifurcation point, the giant cluster is gradually dissolved into a number of small clusters, and the system dynamics is characterized by the integration and separation of the small clusters. Dynamical mechanisms and statistical properties of the nonstationary pattern evolution are analyzed and conducted, and some scalings are newly revealed. Remarkably, it is found that the few active nodes, which escape from the giant cluster with a high frequency, are independent of the coupling strength while are sensitive to the bifurcation types. We hope our findings about nonstationary pattern could give additional understandings to the dynamics of complex systems and have implications to some real problems where systems maintain their normal functions only in the unsynchronizable state.