讲座题目:Decomposition Formula and Stationary Measures for Stochastic Lotka-Volterra Systems with Applications to Turbulent Convection




报告地点: 长江大学东校区8406

专家简介:蒋继发,上海师范大学二级教授,国家有突出贡献的中青年专家,享受国务院特殊津贴;曾获上海市自然科学奖二等奖和安徽省科技进步奖二等奖;一直从事研究生的培养,一名博士生获国家杰出青年科学基金资助,两名博士生获全国优秀博士论文; 分别被评为全国优秀博士论文指导教师和科学院(连续三年)优秀研究生指导教师。

摘要:Motivated by the remarkable works of Busse and his collaborators in the 1980s on turbulent convection in a rotating layer, we explore the long-run behavior of stochastic Lotka-Volterra (LV) systems both in pull-back trajectories and in stationary measures. A decomposition formula is established to describe the relationship between the solutions of stochastic and deterministic LV systems and the stochastic logistic equation. By virtue of this formula, it can be verified that every pull-back omega limit set is an omega limit set of the deterministic LV  system multiplied by the random equilibrium of the stochastic logistic equation. The formula is also used to derive the existence of a stationary measure, its support and ergodicity. The developed theory is successfully utilized to completely classify three dimensional competitive stochastic LV systems into 37 classes. The expected occupation measures weakly converge to a strongly mixing measure and all stationary measures are obtained for each class except class 27 c).  The class 27 c) is an exception, almost every pull-back trajectory  cyclically oscillates around the boundary of the stochastic carrying simplex characterized by three unstable stationary solutions. The limit of the expected occupation measures is neither unique nor ergodic. These are consistent with  symptoms of turbulence.