题目：On the Stochastic Lotka-Volterra Systems with Identical Intrinsic Growth Rates

报告人：蒋继发 （上海师范大学）

时间：2015年3月20日，周五下午2：30―4：00

地点：管理楼 1318

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.

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