Weierstrass Institute for Applied Analysis and Stochastic, Mohrenstrasse 39, 10117 Berlin, Germany.
Phys Rev E. 2017 Nov;96(5-1):052205. doi: 10.1103/PhysRevE.96.052205. Epub 2017 Nov 7.
We investigate the dynamics of a Kuramoto-type system of globally coupled phase oscillators with equidistant natural frequencies and a coupling strength below the synchronization threshold. It turns out that in such cases one can observe a stable regime of sharp pulses in the mean field amplitude with a pulsation frequency given by spacing of the natural frequencies. This resembles a process known as mode locking in lasers and relies on the emergence of a phase relation induced by the nonlinear coupling. We discuss the role of the first and second harmonics in the phase-interaction function for the stability of the pulsations and present various bifurcating dynamical regimes such as periodically and chaotically modulated mode locking, transitions to phase turbulence, and intermittency. Moreover, we study the role of the system size and show that in certain cases one can observe type II supertransients, where the system reaches the globally stable mode-locking solution only after an exponentially long transient of phase turbulence.
我们研究了具有等距自然频率和低于同步阈值的耦合强度的全局耦合相振荡器的 Kuramoto 型系统的动力学。事实证明，在这种情况下，人们可以观察到在平均场幅度中存在稳定的尖锐脉冲状态，其脉动频率由自然频率的间隔给出。这类似于在激光中称为锁模的过程，并且依赖于由非线性耦合引起的相位关系的出现。我们讨论了相相互作用函数中的一阶和二阶谐波在脉冲稳定性中的作用，并呈现了各种分岔动力学状态，例如周期性和混沌调制的锁模、向相湍流的转变和间歇性。此外，我们研究了系统大小的作用，并表明在某些情况下，人们可以观察到 II 型超瞬变，其中系统仅在经历了相湍流的指数长瞬态后才能达到全局稳定的锁模解。
