Stationary Response of Lotka-Volterra System with Real Noises  

作　　者：戚鲁媛 徐伟 高维廷 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University [2]Department of Electronic Information, Northwestern Polytechnical University

出　　处：《Communications in Theoretical Physics》2013年第4期503-509,共7页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos.11172233,10932009,61171155;Natural Science Foundation of Shannxi Province under Grant No.2012JM8010;the Doctorate Foundation of Northwestern Polytechnical University under Grant No.CX201215

摘　　要：A stochastic version of Lotka-Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of It6 stochastic differential equations. The It6 formula is then carried out to obtain the It6 stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged It6 stochastic differential equation of the motion orbit and the corresponding Fokker-Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation.

关 键 词：real noise It5 stochastic differential equation ECOSYSTEM stochastic averaging method 

分 类 号：O211.63[理学—概率论与数理统计]