Sethia Gautam C, Sen Abhijit
Institute for Plasma Research, Bhat, Gandhinagar 382 428, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 2):066203. doi: 10.1103/PhysRevE.84.066203. Epub 2011 Dec 8.
We investigate the existence and stability of traveling-wave solutions in a continuum field of nonlocally 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 multistable regions and illuminates the relative influences of time delay, the nonlocality 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. One 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 nonstationary breather states for this model system that are characterized by periodic oscillations of the complex order parameter.
我们研究了具有距离依赖传播延迟的非局部耦合相同相位振荡器连续场中行波解的存在性和稳定性。给出了系统参数空间中的一个综合稳定性图，该图展示了丰富的多稳态区域结构，并阐明了时间延迟、非局部性参数和固有振荡器频率对这些状态动力学的相对影响。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裂为不相连的区域。对于高连通性，这些区域呈现出舌状结构，而对于低连通性，它们则融入同步状态的稳定区域。一个发现是在参数空间中存在不可能有锁相解的禁区。我们还为该模型系统发现了一类新的非平稳呼吸子状态，其特征是复序参量的周期性振荡。
