The survival analysis for Gallopin's system in a polluted environment

The long-time behavior of the consumer population in a Gallopin's system, l ocated in a polluted environment, was studied. Firstly, a mathematical mode l, i.e., a nonlinear ordinary differential system, was made by faking a con stant catch rate into account in model of MA Zhi-en. Secondly, using the ex tension theorem and the comparison theorem, the bound of the system was est imated. Then, the effect of the pollution on the consumer population was di scussed by the use of calculus and qualitative theory of differential equat ion. Finally, some conditions for weak persistence in the mean and extincti on are found out. The threshold between persistence and extinction can be e stablished in some cases.