当前位置: X-MOL 学术Eur. Phys. J. Spec. Top. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Using phase dynamics to study partial synchrony: three examples
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2021-06-05 , DOI: 10.1140/epjs/s11734-021-00156-3
Erik Teichmann

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.



中文翻译:

使用相位动力学研究部分同步:三个例子

部分同步状态出现在完全同步和异步之间,并表现出许多有趣的特性。最常见的是,在相位近似的框架内研究这些状态。后者普遍用于分析耦合振荡系统。通常,相位动力学描述是在弱耦合极限下获得的,即在耦合强度的一阶中。超出一阶的扩展代表一个未解决的问题,是一个活跃的研究领域。在本文中,三个部分同步状态按复杂性增加的顺序进行了研究和呈现。首先,分析了相位响应曲线用于描述宏观振子的用途。为了达成这个,测量了所有耦合极限循环振荡器模型中的平均场振荡对脉冲刺激的响应。下一部分处理两组 Kuramoto 模型,其中一个吸引组和一个排斥组的相互作用导致一个有趣的孤立状态,位于完全同步和自洽的部分同步之间。在最后一部分中,一个相对简单的三个 Stuart-Landau 振荡器系统的相位动力学扩展到弱耦合极限之外。生成的模型包含高阶相位近似中的三重项,尽管结构连接只是成对的。最后,分析了新项与耦合的缩放。其中一个有吸引力和一个排斥群体的相互作用导致一种有趣的孤立状态,位于完全同步和自洽的部分同步之间。在最后一部分中,一个相对简单的三个 Stuart-Landau 振荡器系统的相位动力学扩展到弱耦合极限之外。生成的模型包含高阶相位近似中的三重项,尽管结构连接只是成对的。最后,分析了新项与耦合的缩放。其中一个有吸引力和一个排斥群体的相互作用导致一种有趣的孤立状态,位于完全同步和自洽的部分同步之间。在最后一部分中,一个相对简单的三个 Stuart-Landau 振荡器系统的相位动力学扩展到弱耦合极限之外。生成的模型包含高阶相位近似中的三重项,尽管结构连接只是成对的。最后,分析了新项与耦合的缩放。虽然结构连接只是成对的。最后,分析了新项与耦合的缩放。虽然结构连接只是成对的。最后,分析了新项与耦合的缩放。

更新日期:2021-06-05
down
wechat
bug