Chen Yuxin, Gemmer John A, Silber Mary, Volkening Alexandria
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60204, USA.
Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, North Carolina 27109, USA.
Chaos. 2019 Apr;29(4):043119. doi: 10.1063/1.5083973.
We consider a periodically forced 1D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that allows us to identify a preferred phase of the forcing when tipping occurs? The quasistatic regime, where the forcing period is long compared to the adiabatic relaxation time, has been well studied; our work instead explores the case when these time scales are comparable. We compute optimal paths using the path integral method incorporating the Onsager-Machlup functional and validate results with Monte Carlo simulations. Results for the preferred tipping phase are compared with the deterministic aspects of the problem. We identify parameter regimes where nullclines, associated with the deterministic problem in a 2D extended phase space, form passageways through which the optimal paths transit. As the nullclines are independent of the relaxation time and the noise strength, this leads to a robust deterministic predictor of the preferred tipping phase in a regime where forcing is neither too fast nor too slow.
我们考虑一个周期性驱动的一维朗之万方程，在无噪声情况下它具有两个稳定的周期解。我们提出这样一个问题：在这些周期解之间是否存在一条最可能的噪声诱导跃迁路径，使我们能够在发生翻转时确定驱动的一个优先相位？与绝热弛豫时间相比驱动周期较长的准静态 regime 已得到充分研究；我们的工作则探索这些时间尺度可比的情况。我们使用包含昂萨格 - 马赫卢普泛函的路径积分方法计算最优路径，并用蒙特卡罗模拟验证结果。将优先翻转相位的结果与问题的确定性方面进行比较。我们确定了参数 regime，在二维扩展相空间中与确定性问题相关的零倾线形成最优路径通过的通道。由于零倾线与弛豫时间和噪声强度无关，这导致在驱动既不太快也不太慢的 regime 中对优先翻转相位有一个稳健的确定性预测器。
