论文标题
关于复杂网络中谐振和同步状态的注释
Notes on Resonant and Synchronized States in Complex Networks
论文作者
论文摘要
网络上的同步和共振是一些最引人注目的集体动力学现象。网络拓扑，或耦合振荡器合奏中连接的性质和分布在塑造这两个现象的局部和全球演化中起着至关重要的作用。本文在紧凑的数学框架内进一步探讨了这种关系，并在某些关键问题上提供了新的贡献，包括在任意拓扑中平均同步时间的封闭限制；这段时间耦合强度的影响的新证据；与拉普拉斯基质的特征值有关共振频率的精确封闭表达式； \ textit {flagencer node}对网络的影响的有效性的度量；最后，讨论了共同同步状态的存在。在同一设置中，也讨论了线性摆动方程解的某些属性。在两个不同的真实网络（一个社交网络和功率网格）上进行的数值实验说明了这些结果的重要性，并阐明了如何在此类网络中解释这些过程的有趣方面。
Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial role in shaping the local and global evolution of the two phenomena. This article further explores this relationship within a compact mathematical framework and provides new contributions on certain pivotal issues, including a closed bound for the average synchronization time in arbitrary topologies; new evidences of the effect of the coupling strength on this time; exact closed expressions for the resonance frequencies in terms of the eigenvalues of the Laplacian matrix; a measure of the effectiveness of an \textit{influencer node}'s impact on the network; and, finally, a discussion on the existence of a resonant synchronized state. Some properties of the solution of the linear swing equation are also discussed within the same setting. Numerical experiments conducted on two distinct real networks - a social network and a power grid - illustrate the significance of these results and shed light on intriguing aspects of how these processes can be interpreted within networks of this kind.
