污染环境下具有脉冲输入环境毒素的恒化器模型的灭绝阈值研究  

Study on Extinction Threshold of a Chemostat Model with Environmental Toxin of Pulse Input in a Polluted Environment

作　　者：王芳[1] 程惠东[1] 

机构地区：[1]山东科技大学理学院,山东青岛266510

出　　处：《山东科技大学学报（自然科学版）》2011年第1期71-77,共7页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：山东科技大学科学研究"春蕾计划"项目(2010AZZ084)

摘　　要：研究了污染环境下具有脉冲输入环境毒素的恒化器模型。利用乘子理论和小振幅扰动法,得到当脉冲输入营养物小于一个临界值或环境毒素的排放量大于一个临界值时,种群灭绝周期解全局渐进稳定的结论,同时得到了种群持久的条件。从生物学观点提出了污染环境下保护物种的方法是改变营养物的输入量或控制环境毒素的排放量。In this paper,a chemostat model with environmental toxin of pulse input in a polluted environment was studied.Using Floquet theory and small amplitude perturbation method,a conclusion was that there existed a global asymptotical stability for periodic solution of population extinction when the impulsive input concentration of nutrients was less than some critical value or the discharge volume of toxicants was larger than some critical value.At the same time,the condition of the population permanence was obtained.From the biological point of view,the method for protecting species is to improve the amount of nutrient input,and control the amount of toxicant input to the chemostat under the polluted environment.

关 键 词：恒化器模型 全局渐近稳定 灭绝 持久 脉冲输入 

分 类 号：O175.2[理学—数学]