摘要翻译：
本文介绍了描述具有不同特征频率的全局耦合振子系统中自同步相变的Kuramoto模型的线性重新表述。重新表述的模型提供了一个可供选择的连贯框架，通过该框架，人们可以分析地解决最初的Kuramoto分析不适合的同步问题。它使我们可以显式地求解1）振子数目有限的系统的全锁相转变临界点（不同于原来的Kuramoto模型，它只能在平均场极限下隐式地求解）和2）一类新的连续统系统的同步序参量和临界点。它还使探索系统走向稳态时的动力学成为可能。虽然本文的讨论仅限于具有全局耦合的系统，但由线性重列所引入的新形式也有助于解决具有局部或非对称耦合的系统。
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英文标题：
《A linear reformulation of the Kuramoto model of self-synchronizing
  oscillators》
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作者：
David C. Roberts
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Pattern Formation and Solitons        图形形成与孤子
分类描述：Pattern formation, coherent structures, solitons
图案形成，相干结构，孤子
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The reformulated model provides an alternative coherent framework through which one can analytically tackle synchronization problems that are not amenable to the original Kuramoto analysis. It allows one to solve explicitly for the synchronization order parameter and the critical point of 1) the full phase-locking transition for a system with a finite number of oscillators (unlike the original Kuramoto model, which is solvable implicitly only in the mean-field limit) and 2) a new class of continuum systems. It also makes it possible to probe the system's dynamics as it moves towards a steady state. While discussion in this paper is restricted to systems with global coupling, the new formalism introduced by the linear reformulation also lends itself to solving systems that exhibit local or asymmetric coupling.
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PDF链接：
https://arxiv.org/pdf/704.1166