Coherence in nonlinear dynamical systems subjected to common fluctuating forcing

在现实世界中，有各种表现出自我维持动态的元素的例子。特别是，产生自维持节律的非线性振荡器在包括物理、化学、生物和工程在内的各个领域中普遍存在。众所周知，周期性的外力可以缠绕驱动振子，相互作用的耦合振子可以表现出相互同步。最近的研究还表明，在共同或相关的随机强迫的驱动下，振荡器表现出同步，或者更广泛地说，是相干的。在本研究项目中，我们从理论上分析了导致这种非平凡现象的机制。具体地说，基于非线性振荡器的相减理论，我们证明了这种噪声诱导的同步现象一般发生在弱驱动振荡器中，并阐明了它的条件。

There are various examples of elements that exhibit self-sustained dynamics in the real world. In particular, nonlinear oscillators that generate self-sustained rhythms are ubiquitous in various fields including physics, chemistry, biology, and engineering. It is well known that periodic external forcing can entrain the driven oscillators and interacting coupled oscillators can exhibit mutual synchronization. Recent studies have also revealed that the oscillators exhibit synchronization, or more generally coherence, when driven by common or correlated stochastic forcing. In this research project, we theoretically analyzed the mechanism leading to such nontrivial phenomena. Specifically, on the basis of the phase-reduction theory for nonlinear oscillators, we showed that such noise-induced synchronization phenomenon generally occurs in weakly driven oscillators and clarified its conditions.