论文标题
非局部耦合的Stuart-Landau振荡器中的非平凡扭曲状态
Nontrivial Twisted States in Nonlocally Coupled Stuart-Landau Oscillators
论文作者
论文摘要
扭曲状态是振荡介质中集体动力学的一种重要但简单的形式。在这里，我们描述了非局部耦合Stuart-Landau振荡器系统中一种非平凡的扭曲状态。非平凡的扭曲状态（NTS）是一个连贯的行驶波，其特征是振幅和相位梯度的不均匀曲线，可以分配一个绕组数。为了进一步研究其特性，采用了几种方法。我们在连续限制中执行线性稳定性分析，并将结果与在有限大小的系统中获得的Lyapunov指数进行比较。协变量lyapunov向量的确定使我们能够识别集体模式。此外，我们表明NTS在固有频率中对小的异质性是可靠的，并进行了分叉分析，表明NTSS在鞍形节点分叉中出生/歼灭，并改变了其在HOPF Bifurcurcations中的稳定性。我们观察到稳定的NTS，绕组1和2。后者在超临界的HopF分叉中可能会失去稳定性，从而导致2-NT的调制。
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.
