非局域耦合Stuart-Landau振子中的非平凡扭曲态
Nontrivial Twisted States in Nonlocally Coupled Stuart-Landau Oscillators
摘要：
扭曲态是振荡介质中集体动力学的一种重要而简单的形式。在这里，我们描述了一个系统的非局部耦合的斯图尔特-朗道振荡器的非平凡类型的扭曲状态。非平凡扭曲态（NTS）是一种相干的行波，其特征在于振幅和相位梯度的不均匀分布，可以分配一个绕组数。为了进一步研究其性质，采用了多种方法。我们进行了线性稳定性分析的连续极限和比较的结果与李雅普诺夫指数在有限大小的系统。协变李雅普诺夫向量的确定使我们能够识别集体模式。此外，我们表明，NTS是强大的小的异质性的固有频率，并提出了一个分叉分析，揭示NTSS出生/湮灭在鞍结分叉和改变其稳定性的Hopf分叉。我们观察到稳定的NTS与绕组数1和2。后者在超临界Hopf分岔中可能失去稳定性，导致调制的2-NTS。
英文摘要：
A twisted state is an important yet simple form of collective dynamics in an oscillatory medium. Here, we describe a nontrivial type of twisted state in a system of nonlocally coupled Stuart-Landau oscillators. The nontrivial twisted state (NTS) is a coherent traveling wave characterized by inhomogeneous profiles of amplitudes and phase gradients, which can be assigned a winding number. To further investigate its properties, several methods are employed. We perform a linear stability analysis in the continuum limit and compare the results with Lyapunov exponents obtained in a finite-size system. The determination of covariant Lyapunov vectors allows us to identify collective modes. Furthermore, we show that the NTS is robust to small heterogeneities in the natural frequencies and present a bifurcation analysis revealing that NTSs are born/annihilated in a saddle-node bifurcation and change their stability in Hopf bifurcations. We observe stable NTSs with winding number 1 and 2. The latter can lose stability in a supercritical Hopf bifurcation, leading to a modulated 2-NTS.
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