Sun Xu, Yang Fang, Sun Thomas
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.
Basic Department, Information Engineering University, Zhengzhou 450001, China.
Chaos. 2024 Jan 1;34(1). doi: 10.1063/5.0180511.
Nonlinear dynamical systems, such as climate systems, often switch from one metastable state to another when subject to noise. The first occurrence of such state transition, which is usually characterized by the first passage time, has gained enormous interest in many engineering and scientific fields. We develop an efficient numerical method to compute the probability density of the first passage time for state transitions in stochastic dynamical systems driven by Brownian motions. The proposed method involves solving a singular integral equation, which determines probability density of the first passage time. Some numerical examples, with application to a simplified thermohaline circulation system, are provided to illustrate and verify the proposed method.
非线性动力系统，如气候系统，在受到噪声影响时常常会从一个亚稳态切换到另一个亚稳态。这种状态转变的首次发生，通常以首次通过时间为特征，在许多工程和科学领域引起了极大的关注。我们开发了一种有效的数值方法来计算由布朗运动驱动的随机动力系统中状态转变的首次通过时间的概率密度。所提出的方法涉及求解一个奇异积分方程，该方程确定首次通过时间的概率密度。提供了一些应用于简化热盐环流系统的数值例子来说明和验证所提出的方法。
