中科院数学与系统科学研究院

数学研究所

动力系统研讨班报告

报告人：    Yao Li(University of Massachusetts Amherst)

题  目：Small noise perturbations of dynamical systems: theory and application

时  间：2018.06.12（星期二）, 15:00-16:00

地  点：数学院南楼N913室

摘 要：

In the first half of this talk I will present some of my recent work about the small noise perturbation problem of dynamical systems. We proved some results about the concentration of the invariant probability measure on “dynamic” neighborhoods of the attractor, which leads to an interesting entropy-dimension relation. Then we will discuss two applications in systems biology and statistical physics. In systems biology, some systematic measures of complex biological systems, including degeneracy, complexity, and robustness, are proposed and intensively studied. With the help of our theoretical results, we can quantify these systematic measures and investigate their connections. The second application is an ongoing big project. The fundamental goal is to derive macroscopic thermodynamic laws from billiards-like deterministic dynamics of kinetic particles. After some computational and rigorous work, this problem is reduced to a stochastic energy exchange model, which is eventually approximated by a stochastic differential equation. We expect to derive various macroscopic thermodynamic laws by applying our theoretical results.