Driven synchronization in random networks of oscillators.
Driven synchronization in random networks of oscillators.
复制标题
振荡器随机网络中的驱动同步。
作者：
J. Hindes;C. Myers
同步是许多非平衡系统中普遍存在的现象。最近对这一领域的兴趣与复杂网络的研究重叠，其中一个主要焦点是确定系统的连接模式如何影响它可以产生的行为类型。到目前为止，建模工作集中在振荡器网络相互同步的趋势上，而不太强调外部驱动的影响。在这项工作中，我们讨论了相互之间的相互作用和驱动同步网络的相振荡器的仓本型，并探讨如何结构和出现这样的国家取决于底层的网络拓扑结构的简单随机网络与给定的度分布。我们发现了各种有趣的动力学行为，包括分叉和双稳态模式是定性不同的异质和同质网络，并分开的Takens-Bogdanov-Cusp奇异性的参数区域中的振荡器之间的耦合强度弱。我们的分析是连接到振荡器集群的重要状态和过渡的基本动力学。
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns affect the types of behavior that it can produce. Thus far, modeling efforts have focused on the tendency of networks of oscillators to mutually synchronize themselves, with less emphasis on the effects of external driving. In this work, we discuss the interplay between mutual and driven synchronization in networks of phase oscillators of the Kuramoto type, and explore how the structure and emergence of such states depend on the underlying network topology for simple random networks with a given degree distribution. We find a variety of interesting dynamical behaviors, including bifurcations and bistability patterns that are qualitatively different for heterogeneous and homogeneous networks, and which are separated by a Takens-Bogdanov-Cusp singularity in the parameter region where the coupling strength between oscillators is weak. Our analysis is connected to the underlying dynamics of oscillator clusters for important states and transitions.