Coherence in nonlinear dynamical systems subjected to common fluctuating forcing

在真实的世界中，有各种各样的元素表现出自我维持的动态。 特别地，产生自我维持的节律的非线性振荡器在包括物理学、化学、生物学和工程学的各个领域中是普遍存在的。 众所周知，周期性的外部强迫可以携带驱动振子和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，振荡器表现出同步性，或更一般的相干性，当驱动共同或相关的随机强迫。 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。 基于非线性振子的相位约化理论，证明了这种噪声诱导的同步现象普遍存在于弱驱动振子中，并阐明了其存在的条件。

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.