We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott–Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.

中文翻译：

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非线性耦合相位振荡器系统中的扭曲态

我们研究具有非线性非局部耦合的同相振荡器环的动力学。使用Ott–Antonsen方法，该问题被公式化为局部复数阶参数的偏导数方程组。在此框架下，我们研究了扭曲状态的存在和稳定性。同时发现了完全相干和部分相干的稳定扭曲状态（对于相同的振荡器，第一次出现了后者）。我们表明，扭曲状态可以从中等长度的某个临界值开始或在长度段上保持稳定。分析结果已通过有限集合中的直接数值模拟得到证实。