ANALYSIS OF A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY  

作　　者：CHUNYANJI DAQING JIANG 

机构地区：[1]School of Mathematics and Statistics, Changshu Institute of Technology Changshu 215500, Jiangsu~ P~ R. China [2]School of Mathematics and Statistics, Northeast Normal University Changchun 130023, Jilin, P. R. China [3]School of Mathematics and Statistics, Northeast Normal University Changchun 130024, Jilin, P. R. China

出　　处：《International Journal of Biomathematics》2013年第3期11-31,共21页生物数学学报（英文版）

摘　　要：In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equi- librium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.

关 键 词：Predator prey model with disease Ito formula STABLE stochastically unsta-ble stochastically stable in the large. 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]