局部吸引子、简并性和解析性：局部耦合Kuramoto模型的对称性效应
Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model
摘要：
本文研究了具有周期边界条件的局部耦合Kuramoto模型。我们的主要目标是展示如何从对称性假设中获得解析解，当我们继续努力时，除了局部吸引子的存在外，我们还展示了对称性导致的一些意想不到的特征，如间歇性和混沌周期相位滑移，稳定解的退化和双分叉组合。作为我们的分析结果，我们表明，稳定的不动点的同步区域中可能会得到只有少量的现有的解决方案，并为一类的固有频率配置，我们显示的临界同步耦合作为一个函数的振荡器的数量，精确和渐近的解析表达式。
英文摘要：
In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
