GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT

被引:100
作者
Meng, Xinzhu [1 ,2 ,3 ]
Wang, Lu [3 ]
Zhang, Tonghua [4 ]
机构
[1] Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control Shan, Qingdao 266590, Peoples R China
[2] Shandong Univ Sci & Technol, Minist Sci & Technol, Qingdao 266590, Peoples R China
[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[4] Swinburne Univ Technol, Dept Math, Hawthorn, Vic 3122, Australia
来源
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2016年 / 6卷 / 03期
基金
中国国家自然科学基金;
关键词
Stochastic chemostat model; impulsive stochastic differential equations; extinction; permanence in mean; saturated growth rate; TOXICANT INPUT; MODEL; POPULATIONS; PERSISTENCE; DELAYS;
D O I
10.11948/2016055
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.
引用
收藏
页码:865 / 875
页数:11
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