| This paper mainly studies the mathematical model of two different populations in the pollution of the environment, research and analysis of the dynamical behavior of these models by a mathematical method of dynamics.In this paper, a total of four chapters:The first chapter introduces the research background, status and significance of the predator- prey food chain model, then gives some basic predator- prey dynamics mathematical model and introduces several types of models of this paper.The second chapter studies the toxin in pulse input pollution of ecological environment, to discuss the model of the predator predator-prey system with stage structure. Fully using the theorem to prove that the delay periodic solution of the system is global, the permanent survivability and population.The third chapter considers the population infected with certain diseases and human killing, we formulated by continuous and pulse external factors such as the epidemic model of two kinds of pollution, and to study the dynamic behavior of the system. Assume that humans only kill susceptible population, is in a continuous system, we obtain sufficient conditions for the boundedness of finally, solutions and global asymptotic stability of equilibrium point. In the pulse system, by using the analysis method of the comparison theorem, to prove that the disease-free periodic solution under different conditions of global asymptotic attraction, as well as the system is permanent survivability. The fourth chapter of this paper summarizes and proposes to study the contents of the overview in the future. |
