【直播】【兰州大学兰州理论物理中心（筹）】哈佛大学郑宇成：Stochastic limit-cycle …

本系列报告由兰州大学兰州理论物理中心（筹）主办，于2021年10月30日10:00开始，授权蔻享学术进行网络直播。

Stochastic limit-cycle oscillations of a nonlinear system under random perturbations

报告人

郑宇成 博士（哈佛大学）

时间

2021年10月30日 10:00

报告摘要

Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a time-inhomogeneous Gaussian process, near a deterministic limit cycle in $\mathbb{R}^n$. Based on  respectively the theory of random perturbations of dynamical systems and the WKB approximation that codes the large deviations principle (LDP), results are developed in parallel from both standpoints of stochastic trajectories and transition probability density and their relations are elucidated.  We show rigorously the correspondence between the local Gaussian fluctuations and the curvature of the large deviation rate function near its infimum, connecting the CLT and the LDP of diffusion processes. We study uniform asymptotic behavior of stochastic limit cycles through the interchange of limits of time $t\to\infty$ and $\epsilon\to 0$. Three further characterizations of stochastic limit cycle oscillators are obtained: (i) An approximation of the probability flux near the cycle; (ii) Two special features of the vector field for the cyclic motion; (iii) A local entropy balance equation along the cycle with clear physical meanings. Lastly and different from the standard treatment, the origin of the $\epsilon$ in the theory is justified by a novel scaling hypothesis via constructing a sequence of stochastic differential equations.

报告人介绍

郑宇成，博士毕业于美国华盛顿大学应用数学系，导师为钱纮教授。2010年毕业于台北医学大学医学系，通过医师专业考试后于台北新光医院担任医师。2012年赴美留学，于2014年硕士毕业于美国密歇根大学生物医学工程专业。博士期间主要研究方向为生物数学和数学物理，包括概率论、随机过程和大偏差理论在统计物理以及生物物理上的应用。目前在哈佛大学从事博士后研究，主要研究方向为动力系统以及随机过程在癌症演化上的应用。

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