标题： 局部吸引子、退化性和解析性：对称性在局部耦合的Kuramoto模型中的影响 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，我们研究带有周期性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，而在我们进行这一研究的过程中，除了展示局部吸引子的存在外，还展示了一些由于对称性性质而产生的意外特征，例如间歇性和混沌的周期相位滑移、稳定解的退化以及双分岔组合。通过我们的分析，我们表明在同步区域内，仅需少量现有的解即可获得稳定的固定点，并且对于一类自然频率配置，我们展示了同步临界耦合的解析表达式，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 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.