Exit Time from the perspective of random dynamical systems and its application in stochastic resonance

随机动力系统视角下的退出时间及其在随机共振中的应用

• 批准号: 2752048
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2752048
• 关键词: Exit; Time; perspective; random; dynamical

The exit time problem, or first passage time problem, typically involves determining the time it takes for a stochastic process (such as Brownian motion or Lévy motion) to leave a given domain. More specifically, it deals with calculating the probability distribution of the time it takes for a diffusion process to first reach the boundary of a bounded domain, starting from an initial point within that domain. We consider deterministic quantities in this problem because they can provide us with the dynamical information of random systems, that is, how the system evolves over time, and quantifying the dynamic behavior of random systems helps people understand how randomness affects these systems. People mainly consider the mean exit time and escape probability in the exit time problem. Mean exit time quantifies how long a random system will stay in a region, while escape probability describes the likelihood of the system transitioning from one region to another. The exit time problem has a wide range of applications in many fields, such as the time of a fund going bankrupt, the time it takes for a Brownian dust particle to escape from a region, the time for a protein molecule to gain sufficient energy to change shape and activate a biological process, and the time when the population of a species in ecology falls below a critical threshold, etc. One important and intriguing application of the exit time problem is stochastic resonance, the simplest example being the addition of a periodic force to a bistable system in addition to stochastic forces. In such a scenario, there exists an optimal noise intensity that, in conjunction with the periodic force, allows the system to escape from one metastable state to another with near-perfect precision within one period, meaning the mean exit time is half the period. This noise intensity is also when the signal-to-noise ratio of the system's output is maximized. This phenomenon, where noise enhances the signal under the influence of periodic forcing, is known as stochastic resonance. Stochastic resonance has widespread applications in engineering, most notably in the detection of weak signals, that is, extracting useful signals from a strong noise background or detecting extremely faint signals. By considering the exit time to find the optimal noise intensity and thus enhance the output noise, we grasp a significant value of studying the exit time problem.

退出时间问题或第一次通过时间问题rllévy运动）要更具体地离开给定的域，它可以从一个有限域的边界来计算其扩散过程所需的时间的概率分布在这个问题中，thain中的初始点可以为我们提供随机系统的动态信息，即它们的系统如何随着时间的流逝而演变，并量化RRP的动态行为有助于人们了解随机的THESESS系统出口时间问题的平均退出时间和逃避概率，而概率描述了从一个领域过渡到另一个领域的f应用程序。灰尘粒子从生态学中的物种种群降至临界阈值以下等区域时间。地址。在这种情况下。同样，当系统的输出的信号与噪声比率最大化时，时间，定期强迫下的信号被称为随机共鸣。通过退出时间来找到最佳的噪声，即研究出口时间问题的输出噪声t值。