In this paper, the population dynamics models including the Environmental problems is of paramount importance which is the issue of controlling the population size of living organisms in complex ecological systems has become urgent. Mathematical models are needed that allow one to assess the possible consequences of human impact on nature and organize his activities in such a way as to prevent an “ecological catastrophe. Such problems can be solved if a mathematical model corresponding to the required situation is analyzed. In this work, we built, solved, and also investigated a model of unlimited population growth, a model of the predator-prey system according to the Lotka-Volterra problem.