A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively...A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.展开更多
We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. The model consists of three ordinary differential equations： one for the p...We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. The model consists of three ordinary differential equations： one for the population density, one for the amount of toxicant inside the living organisms, and one for the amount of toxicant in the environment. We derive sufficient conditions for the persistence and the extinction of the population depending on the exogenous input rate of the toxicant into the environment and the level of pollution tolerance of the organisms. Numerical simulations are carried out to illustrate our main results.展开更多
The long_time behavior of the consumer population in a Gallopin's system, located in a polluted environment, was studied. Firstly, a mathematical model, i.e.,a nonlinear ordinary differential system, was made ...The long_time behavior of the consumer population in a Gallopin's system, located in a polluted environment, was studied. Firstly, a mathematical model, i.e.,a nonlinear ordinary differential system, was made by taking a constant catch rate into account in model of MA Zhi_en. Secondly, using the extension theorem and the comparison theorem, the bound of the system was estimated. Then, the effect of the pollution on the consumer population was discussed by the use of calculus and qualitative theory of differential equation. Finally, some conditions for weak persistence in the mean and extinction are found out. The threshold between persistence and extinction can be established in some cases.展开更多
文摘A predator-prey system in a polluted environment is studied in this paper.Surveying the transformation of toxicants from prey to predator and the effects of toxicants on functional response of predator comprehensively, the thresholds between the weak persistence in the mean and extinction of populations are established.
基金Supported by National Natural Science Foundation of China(No.11201075)Natural Science Foundation of Fujian Province(No.2016J01015)Scholarship under Education Department of Fujian Province
文摘We study a model for the long-term behavior of a single-species population with some degree of pollution tolerance in a polluted environment. The model consists of three ordinary differential equations： one for the population density, one for the amount of toxicant inside the living organisms, and one for the amount of toxicant in the environment. We derive sufficient conditions for the persistence and the extinction of the population depending on the exogenous input rate of the toxicant into the environment and the level of pollution tolerance of the organisms. Numerical simulations are carried out to illustrate our main results.
文摘The long_time behavior of the consumer population in a Gallopin's system, located in a polluted environment, was studied. Firstly, a mathematical model, i.e.,a nonlinear ordinary differential system, was made by taking a constant catch rate into account in model of MA Zhi_en. Secondly, using the extension theorem and the comparison theorem, the bound of the system was estimated. Then, the effect of the pollution on the consumer population was discussed by the use of calculus and qualitative theory of differential equation. Finally, some conditions for weak persistence in the mean and extinction are found out. The threshold between persistence and extinction can be established in some cases.
基金The National Natural Science Foundation of P.R.China (No.10171010) the Key Project on Scienceand Technology of the Education Ministry of People’s Republic of China (No.Key 01061).
