Mathematical Research On A Pest-Control Model In A Polluted Environment

With the rapid development of industrialization and urbanization, many environmental problems from recessive into dominant and from behind into the front, environmental problems have become important factors of restricting healthy development of economic society. In this thesis, based on the serious environment pollution, we establish a pest-control model in a polluted environment and study the dynamics of such system.In chapter 1, we introduce the background and give some relevant preliminaries. In chapter 2, we formulate a pest-control Gompertz model in a polluted environment with pulse pollutant input and pest killed at different fixed time. The natural enemy amount is decreasing associated with the uptake of pollution. By using stability theory and comparison theorem, sufficient conditions for the global attractiveness of the natural enemy-extinction periodic solution and permanent are obtained. The numerical simulations confirm our theoretical results.In chapter 3, we discuss the dynamics of a stage structured pest control model in a polluted environment with pulse pollution input. The natural enemy is stage structured and only adult predators feed on pests. Assuming that only nature enemy affected by pollutant and pests are caught impulsively, we discuss the dynamics of the model systematically. It is shown that impulsive period, the amount of pollution input and the catching rate of pests can bring obvious effects on the dynamics of system. The sufficient conditions for the global attractivity of the'natural enemy-extinction'periodic solution and permanence of the system are obtained. The numerical simulations verify the theoretical results.