The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramoto type lattice model on a regular ring lattice with the equal spacing assuming that each oscillator has an internal energy (temperature). Our lattice model is derived from the thermodynamical Cucker-Smale model for flocking on the 2D free space under the assumption that the ratio between velocity field and temperature field at each lattice point has a uniform magnitude over lattice points. The proposed model satisfies an entropy principle and exhibits emergent dynamics under some sufficient frameworks formulated in terms of initial data and system parameters. Moreover, the phase-field tends to the Kuramoto phase-field asymptotically.

中文翻译：

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热力学 Kuramoto 系综在规则环格上的涌现行为

受温度场影响的仓本振子的时间演化经常出现在生物振子系综中。在本文中，假设每个振荡器都有一个内能（温度），我们在等间距的规则环晶格上提出了一个广义 Kuramoto 型晶格模型。我们的晶格模型源自热力学 Cucker-Smale 模型，用于在 2D 自由空间上植绒，前提是每个晶格点的速度场和温度场之间的比率在晶格点上具有均匀的大小。所提出的模型满足熵原理，并在根据初始数据和系统参数制定的一些充分框架下表现出紧急动力学。此外，相场渐近地趋向于仓本相场。