Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27517, USA.
Renaissance Computing Institute, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27517, USA.
Chaos. 2023 Jan;33(1):013119. doi: 10.1063/5.0129341.
Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at which rate-induced tipping would occur. Moreover, it does so with significantly increased probability over the noise acting alone. We achieve this by finding a global minimizer in a canonical problem of the Freidlin-Wentzell action functional of large deviation theory that represents the most probable path for tipping. This is realized as a heteroclinic connection for the Euler-Lagrange system associated with the Freidlin-Wentzell action and we find it exists for all rates less than or equal to the critical rate. Its role as the most probable path is corroborated by direct Monte Carlo simulations.
当斜坡参数变化得足够快以至于系统在共存的、吸引的状态之间发生倾斜时，就会发生速率诱导倾斜。我们表明，向系统中添加噪声会导致其在低于速率诱导倾斜发生的临界速率的情况下发生倾斜。而且，与噪声单独作用相比，其发生的概率显著增加。我们通过在代表倾斜最可能路径的大偏差理论的 Freidlin-Wentzell 作用泛函的典型问题中找到全局最小化来实现这一点。这是通过与 Freidlin-Wentzell 作用相关的 Euler-Lagrange 系统的异宿连接来实现的，我们发现它存在于所有小于或等于临界速率的速率下。它作为最可能路径的作用通过直接的蒙特卡罗模拟得到证实。
