标题： 时间尺度和拓扑结构在复杂网络动力学中的作用 显示英文标题

标题： Role of time scales and topology on the dynamics of complex networks

摘要： 时间尺度与非线性振荡器复杂网络结构特性之间的相互作用可以产生许多有趣的现象，如振幅死亡、簇同步、频率同步等。 我们通过考虑一个动力系统复杂网络来研究这些现象的出现及其转变，其中一部分系统在网络中以较慢的时间尺度演化。 我们报告了整个网络向振幅死亡的转变以及当连接模式变化时转变附近的标度行为。 我们还讨论了振荡的抑制与恢复以及随着慢系统数量增加时的交叉行为。 通过考虑具有多时间尺度的无标度网络，我们研究了链接结构异质性在动态特性和相应临界行为中的作用。 在这种情况下，中心节点被变慢，我们的主要结果是当缓慢性在网络中扩散时完全同步丧失的逃逸时间统计以及整个网络自组织到新的频率同步状态。 我们的结果在由异质振荡器组成的生物、物理和工程网络中具有潜在的应用价值。 显示英文摘要

摘要： The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the cross over behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.