LIMSI-CNRS, Université Paris Saclay, F-91405 Orsay, France.
Institute of Mathematics and Centre for Medical and Biotechnical Research, Academy of Sciences of Ukraine, Kyiv, Ukraine.
Chaos. 2019 Dec;29(12):121103. doi: 10.1063/1.5125119.
Synchronization of a large ensemble of identical phase oscillators with a nonlocal kernel and a phase lag parameter α is investigated for the classical Kuramoto-Sakaguchi model on a ring. We demonstrate, for low enough coupling radius r and α below π/2, a phase transition between coherence and phase turbulence via so-called defect states, which arise at the early stage of the transition. The defect states are a novel object resulting from the concatenation of two or more uniformly twisted waves with different wavenumbers. Upon further increase of α, defects lose their stability and give rise to spatiotemporal intermittency, resulting eventually in developed phase turbulence. Simulations close to the thermodynamic limit indicate that this phase transition is characterized by nonuniversal critical exponents.
我们研究了具有非局部核和相位滞后参数 α 的大量相同相位振荡器的同步问题，针对的是环上的经典 Kuramoto-Sakaguchi 模型。我们证明，在足够低的耦合半径 r 和低于 π/2 的 α 下，通过所谓的缺陷态，在相变的早期，相干和相湍流之间会发生相变。缺陷态是由两个或更多具有不同波数的均匀扭曲波串联而成的一种新的物体。随着 α 的进一步增加，缺陷态失去稳定性，导致时空间歇性，最终导致发展中的相湍流。接近热力学极限的模拟表明，这种相变的特征是非普适的临界指数。
