具有传播时滞的非局域耦合相位振子环中行波态的存在性和稳定性
Existence and stability of travelling wave states in a ring of non-locally coupled phase oscillators with propagation delays
摘要：
研究了具有距离依赖传播时滞的非局部耦合同相振子在连续场中行波解的存在性和稳定性。在参数空间的系统，显示了丰富的多稳定区域的结构和照明的相对影响的时间延迟，非局部性参数和本征振荡器频率上的动态这些状态的一个全面的稳定图。固有振荡器频率的降低导致行波的稳定域在参数空间中分解成不连续的区域。这些区域表现出高连通性的舌头结构，而它们进入低连通性的同步状态的稳定区域。一个新的发现是在参数空间中存在的禁区，没有锁相解决方案是可能的。我们还发现了一类新的非定常\textit{breather}状态，其特征在于复杂的序参量的周期振荡的模型系统。
英文摘要：
We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric space of the system is presented that shows a rich structure of multi-stable regions and illuminates the relative influences of time delay, the non-locality parameter and the intrinsic oscillator frequency on the dynamics of these states. A decrease in the intrinsic oscillator frequency leads to a break-up of the stability domains of the traveling waves into disconnected regions in the parametric space. These regions exhibit a tongue structure for high connectivity whereas they submerge into the stable region of the synchronous state for low connectivity. A novel finding is the existence of forbidden regions in the parametric space where no phase-locked solutions are possible. We also discover a new class of non-stationary \textit{breather} states for this model system that are characterized by periodic oscillations of the complex order parameter.
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