Dynamics of a prey-predator system under Poisson white noise excitation  

作　　者：Shan-Shan Pan Wei-Qiu Zhu 

机构地区：[1]Department of Mechanics,State Key Lab of Fluid Power Transmission and Control,Zhejiang University

出　　处：《Acta Mechanica Sinica》2014年第5期739-745,共7页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(10932009,11072212,11272279,and 11321202)

摘　　要：The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.

关 键 词：Prey-predator ecosystem Poisson white noise Stochastic averaging- Approximate stationary solution. Per turbation method 

分 类 号：O175[理学—数学]