Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization.
复制标题
Harary 图的奇异平衡和新的同步最小度下界。
作者：
E. Canale;Pablo Monzón
本文研究了均匀（等频率）仓本弱耦合振子模型平衡点的稳定性。2012年[R. Taylor，J. Phys. A：Math. Theor. 45，1-15（2012）]中，根据图的最小度阶比找到了几乎全局同步的充分条件。在这项工作中，一个新的下限，这个比率。改进是通过一个具体的无穷序列的正则图。此外，Wiley等人[Chaos 16，015103（2006）]研究的图的非标准不稳定平衡点被证明存在。
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.