报告人：蒋继发 (上海师范大学)

报告题目：The Decomposition Formula and Stationary Measures for Stochastic Lotka-Volterra Systems with Applications to Turbulent Convection

报告摘要：Motivated by the work of Busse et al. on turbulent convection in a rotating layer, we exploit the long-run behavior for stochastic Lotka-Volterra (LV) systems both in pullback trajectory and in stationary measure. It is proved stochastic decomposition formula describing the relation between solutions of stochastic and deterministic LV systems and stochastic Logistic equation. By virtue of this formula, it is verified that every pull-back omega limit set is an omega limit set for deterministic LV systems multiplied by the random equilibrium of the stochastic Logistic equation. This formula is used to derive the existence of a stationary measure, its support and ergodicity. We prove the tightness for the set of stationary measures and the invariance for their weak limits as the noise intensity vanishes, whose supports are contained in the Birkhoff center. The developed theory is successfully utilized to completely classify three dimensional competitive stochastic LV systems into 37 classes. Time average probability measures weakly converges to an ergodic stationary measure on the attracting domain of an omega limit set in all classes except class 27 c). Among them there are two classes possessing a continuum of random closed orbits and ergodic stationary measures supported in cone surfaces, which weakly converge to the Haar measures of periodic orbits as the noise intensity vanishes. In the exceptional class, almost every pull-back trajectory cyclically oscillates around the boundary of the stochastic carrying simplex characterized by three unstable stationary solutions. The limit for the time average probability measures is neither unique nor ergodic. These are subject to turbulent characteristics.

This is a joint work with Drs. Chen Lifeng and Niu Lei, Profs. Dong Zhao and Zhai Jianliang.

报告人简介: 蒋继发, 1989年7月于中国科学院数学研究所获博士学位, 获首届中国科学院院长奖学金特别奖. 1989年8月至1994年12月在安徽师范大学数学系任教, 自1991底任教授和系副主任. 1995年元月至2004年8月任职于中国科学技术大学数学系, 基础数学博士点博士生导师, 交叉学科生物数学博士点的负责人和博士生导师. 2004年9月通过同济大学全球招聘, 调入同济大学数学系任主任, 工作至2008年2月. 在其期间亲自组织了数学学科一级学科博士点的申报，并作为整个队伍的第一学科带头人, 结果成功获得; 其后, 亲自组织同济大学《基础数学》重点学科的申请，并作为三个主要研究方向的带头人之一。最终获得了重点培育学科. 在2005-2008年间任数学一级学科负责人, 并任二级教授. 2008年3月至今任职于上海师范大学数理学院, 为应用数学博士点的负责人.自从1993年以来持续主持国家自然科学基金委面上项目、参加两项国家自然科学基金委重点项目；主持多项国家教委（教育部）、科学院、上海市科委和教委项目.

报告时间：2017年6月27日（星期二）下午4：00--5：00
报告地点：科技楼南楼602