报告题目: On Asymptotic Measure of Quasi-Potential Systems with Applications to Stochastic Bifurcations
时 间：2023年1月13日（星期五）上午10：00
地 点：腾讯会议（ID：290-456-511）
主 办：数学与统计学院
参加对象：统计系老师与学生
报告摘要：The asymptotic measure of stationary measures for a gradient system under small additive noise perturbation is concentrated on the global minima set of the potential function. Hwang (1980) and Huang et al.(2016) determined the weights of the asymptotic measure supported on equilibria if the global minima set consists of only finite points at which the first nonzero homogeneous polynomials of Taylor expansions are even order. This talk will focus on the asymptotic measure problem of a quasi-potential system which is the orthogonal sum of a gradient system and a divergence-free system. It is given that stationary measures of the gradient system and the quasi-potential system under the same additive noise perturbation admit the same density. We also provide orthogonal group invariance criterion of the density, which helps us to determine the supporting components' weights. Combining these with the global dynamics of quasi-potential system, we give exact asymptotic measure and its support, including stable equilibria, stable periodic orbits, saddles, and chaotic motions et al., of a large number of quasi-potential systems, which are used to study stochastic bifurcations of two or three dimensional quasi-potential systems. Finally, we present Freidlin and Wentzell's method to compute the transitive difficulty matrix and apply it to determine the asymptotic measure and asymptotic limits of solutions of the Cauchy problem for reaction-diffusion equation with small diffusion coefficient.
This is a joint work with Chen Lifeng.
报告人简介：蒋继发，上海师大数理学院博士生导师，二级教授，被国家人事部授予具有突出贡献的中青年专家，享受国务院政府特殊津贴。曾在中国科学技术大学和同济大学任教，获得安徽省科技进步奖和上海市自然科学奖二等奖各一项。曾培养两名博士生入选教育部全国百篇优秀博士论文，曾连续三年被中科院评为“优秀研究生指导导师”。