论文标题
常规环晶格上热力学库拉莫托合奏的紧急行为
Emergent behaviors of Thermodynamic Kuramoto ensemble on a regular ring lattice
论文作者
论文摘要
受温度场影响的库拉莫托振荡器的时间演变通常出现在生物振荡器集合中。在本文中，我们在常规环晶格上提出了一个广义的库拉莫托型晶格模型，其间距相等，假设每个振荡器都有内部能量（温度）。我们的晶格模型来自热力学cucker-smale模型，用于在2D自由空间上蜂拥而至，假设每个晶格点的速度场和温度场之间的比率比晶格点具有均匀的幅度。所提出的模型满足熵原理，并在一些以初始数据和系统参数方面提出的足够框架下展示了新兴的动态。此外，相田渐近地倾向于库拉莫托相。
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.
