Abstract

We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of the long-term evolution of such a system. We have obtained homogeneous, twisted, and nonhomogeneous stationary solutions to the Ott–Antonsen equations corresponding to key variants of the realized collective rotational motion of elements of the medium in question with nonzero mesoscopic characteristics determining the degree of coherence of the dynamics of neighboring particles. We have described the procedures of the search for the class of nonhomogeneous solutions as stationary points of the auxiliary point map and of determining the stability based on analysis of the eigenvalue spectrum of the composite operator. Static and breather cluster regimes have been demonstrated and described, as well as the regimes with an irregular behavior of averaged complex fields including, in particular, the local order parameter.

中文翻译：

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仓本-巴托托克系统中的非时变振荡器的时空体制

摘要

我们考虑了一组非局部耦合的不同相位振荡器的时空状态，它们对应于这种系统长期演进的不同机制。我们已经获得了Ott–Antonsen方程的齐次，扭曲和非齐次平稳解，这些解对应于所讨论介质元素的实现的集体旋​​转运动的关键变体，具有非零介观特性，确定了相邻粒子动力学的相干程度。我们已经描述了搜索作为辅助点图的固定点的非均匀解类的过程以及基于对复合算子特征值谱的分析来确定稳定性的过程。静态和呼吸簇的状态已得到证明和描述，