局部耦合图上带阻挫的惯性 Kuramoto 模型的涌现动力学
Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph
AI总结：
本文研究对称连通网络下带阻挫的惯性 Kuramoto 振荡器的同步问题，通过构建振荡器凸组合与新能量函数推导一阶耗散微分不等式，证明了频率同步可指数级快速涌现。
摘要：
我们研究了对称连通网络下带阻挫效应的惯性 Kuramoto 振荡器的同步行为。由于缺乏二阶梯度流结构且直径二阶导数存在奇异性，我们转而构建振荡器的凸组合及相关新能量函数来控制相位和频率直径。在初始数据和系统参数的充分框架下，我们推导出所构建能量函数的一阶耗散微分不等式。这最终促成了频率同步以指数级速度快速涌现。
英文摘要：
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of diameter, we shift to construct convex combinations of oscillators and related new energy functions that can control the phase and frequency diameters. Under sufficient frameworks on initial data and system parameters, we derive first-order dissipative differential inequalities of constructed energy functions. This eventually gives rise to the emergence of frequency synchronization exponentially fast.
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