Study On The Nonautonomous Periodic Integrated Pest Management Model Under The Influence Of Pesticide Function

The occurrence of pests often causes serious ecological and economic problems,so it is very important to manage the pests which affect human production,life activities and social development.In recent years,mathematical models are used to simulate the pest management process and combine with a comprehensive control program.In order to accurately determine the time of strategy implementation of the pest control,we not only make sure the relationship between pests,natural enemies and pesticides,but also consider the residual effect of pesticides.At the same time,the growth of the population is affected by the seasonal fluctuation factors such as seaso n,climate and food.Therefore,it is necessary to consider the population dynamics model in the periodic environment when we study the population growth and the pest management.In this paper,the residual effect of the insecticide is introduced into the pest control models.According to the theoretical knowledge of impulsive equation,nonautonomous differential equation and comparison theorem,the dynamics of such model are analyzed systematically,and we find the main factors which affect the pest control.In chapter 1,the biological background and the development status of pests systematically are introduced,and some relative preliminaries are given.In chapter 2,a nonautonomous pest control model with the biological control and the chemical control is established.At the same time,the residual effect of insecticide is introduced into the model.The effective killing rate of the insecticide is described by constructing a continuous exponential function which is related to the killing rate,dose,spraying period of pesticide.The sufficient conditions of the global asymptotic stability of the pest eradication periodic solution and the permanence of the system are given.In Chapter 3,considering that pesticides are firstly sprayed in the environment,then act on pests and natural enemies.It is consistent with the pollutant emission model with pulse input toxin.So we mix the two models to be nested and study the effects of the pesticide function on pest and natural enemies.Some related dynamics of the model is analyzed.In chapter 4,the correctness of the theoretical results is verified by numerical simulations.Some factors that relate to the pest management are obtained by analyzing the sensitivity of the parameters.Our results provide a theoretical basis for designing a more reasonable integrated pest management.