标题： 局部吸引子、退化性和解析性：对称性对局部耦合 Kuramoto 模型的影响 显示英文标题

标题： Local attractors, degeneracy and analyticity: symmetry effects on the locally coupled Kuramoto model

摘要： 在本工作中，我们研究具有周期性边界条件的局部耦合 Kuramoto 模型（LCKM）。 我们的主要目标是展示如何从对称性假设中获得解析解，而在我们进行这一努力的过程中，我们展示了由对称性特性引起的某些意外现象：同步区域内局部吸引子的存在；穿越固定点的稳定性交换；固定点稳定性依赖于流形维度；混沌周期和间歇相位滑移。 通过我们的分析，我们表明，在同步区域内仅需少量现有解即可获得稳定的固定点，并且对于一类自然频率配置，我们展示了临界同步耦合的解析表达式，作为振荡器数量的函数，包括精确和渐近形式。 显示英文摘要

摘要： In this work we study the local coupled Kuramoto model (LCKM) 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 some unexpected phenomena resulting from the symmetry properties: the existence of local attractors in the synchronized region; stability exchange for crossing fixed points; fixed point stability dependent on the manifold dimension; chaotic period and intermittent phase slips. 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.