QUALITATIVE ANALYSIS OF A STOCHASTIC PREDATOR-PREY SYSTEM WITH DISEASE IN THE PREDATOR  

作　　者：SHUANG LI XINAN ZHANG 

机构地区：[1]School of Mathematics and Statistics, Central China Normal University Wuhan 430079, Hubei, P. R. China [2]Department of Mathematics, Xinxiang University Xinxiang 453000, Henan, P. R. China [3]School of Mathematics and Statistics, Central China Normal University Wuhan 430079, Hubci, P. R. China

出　　处：《International Journal of Biomathematics》2013年第1期115-127,共13页生物数学学报（英文版）

摘　　要：A stochastic predator prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the determin- istic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large envi- ronmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.

关 键 词：PREDATOR-PREY stochastic perturbation stationary distribution stability extinct. 

分 类 号：Q141[生物学—生态学] TP271[生物学—普通生物学]