The Survival Analysis for Gallopin’s System in a Polluted Environment

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.