应理学院数学系魏俊杰教授邀请，上海师范大学蒋继发教授将来我校进行学术访问，欢迎有兴趣的师生参加。学术报告信息如下：

报告时间：2015年7月21日上午9点

报告地点：H楼447

主 讲 人：蒋继发教授

内容摘要： We exploit the long-run behavior for Lotka-Volterra Stratonovich SDEs with identical intrinsic growth rates. It is first proved that every solution process for the considered SDEs is expressed in terms of a solution for the corresponding  Lotka-Volterra system without noise perturbation multiplied by an appropriate solution process of the scalar logistic equation with the same type noise perturbation.  Then we will present the result on  invariant measures and study their weak convergence as the intensity for the noise tends to zero, we still investigate the weak convergence for the transition probability function of solution process as the time tends to infinity. In particular, we provide the necessary and sufficient conditions for Markov semigroup to have a unique and ergodic invariant measure. Finally we provide the complete dynamics classification for three dimensional competitive Lotka-Volterra Stratonovich SDEs with identical intrinsic growth rates in terms of  pull-back solution flow. There are exactly 37 dynamic scenrios in competitive coefficients. Among them,  each pull-back trajectory in 34 classes is asymptotically stationary, but possibly different stationary solution for different trajectory in same class. There are exact three classes for their limiting behaviors not to be stationary, one of which cyclically oscillates. This is a stochastic version for so called statistical limit cycle and shows that the turbulence in a fluid layer heated from below and rotating about a vertical axis is robust under stochastic disturbances. 

主讲人简介：

蒋继发，上海师范大学数学系教授、博导，人事部有突出贡献的中青年专家，享受国务院特殊津贴。“非线性常微分方程的渐近性态”获安徽省科技进步二等奖（独立承担）。独立培养的第一个和第二个博士分别入选2004年和2006年全国百篇优秀博士学位论文。先后主持国家自然科学基金项目4项，已发表80余篇研究论文。研究方向为微分方程与动力系统。在J.ReineAngewMath.，Trans.AMS.，J.Diff.Equns.，Nonlinearity，SIAMJ.Math.Anal.，SIAMJ.Appl.Math.， J.Math.Biol.，DCDS等国际重要SCI刊物上发表论文60余篇，被SCI学术期刊他人引用超过130篇次。主要学术贡献有：完美地解决了M.W.Hirsch的一个稳定性猜测，并进一步发展成被国际同行评述为“ingenious”的方法，在最弱的条件下，证明了自治/周期/几乎周期的PDEs，ODEs，FDEs和抽象映射的轨线的收敛性。这项成果及其方法被不同领域（包括动力系统、非线性分析、控制论和生物或生态）的学者引用40篇次；精细描述了单调动力系统吸引子的结构；（合作）解决了H.L.Smith提出的竞争映射的“负载单形”唯一性猜测和光滑性等公开问题；（合作）解决了Capasso等提出的“鞍点结构”猜测等。