Pests Management Concerning Impulsive Differential Equation

It is known to all that the management of biological populations is to control the number of a population or some populations, especially control pests according to the need of human de-velopment, ecology and so on. People increasingly realize that it is the proper method to control the number of pests only when the number reaches the Economic Threshold. How to minimize the damage caused by harmful pests and carriers to plants and animals has been a concern for people. Based on the Impulsive Differential Dynamic System, due to the fact that the unreason-able use of pesticide causes pest attacks to occur frequently and rampantly, the environment is polluted and resources are wasted, this paper uses a single-species pest management model with stage structure, multi-population pest-enemy model, and pest-enemy model of pests' reaction to the dose of pesticide and increase of pests' resistance, presents new standpoints and provides the corresponding Policy for the research on pest control.Chapter 2 considers a stage-structured pest control model with impulse effects by state feedback control and suggests controlling the total number of the adults and larvae and that chemical control be used when pests reach the Economic Threshold. Firstly, a semi-continuous dynamic system and its successor functions are given. By adopting the successive function method, we obtain the sufficient conditions of the existence and attractiveness of order one periodic solution. Next, numerical simulation further verifies the theoretical result, which can be comprehended visually.Chapter 3 establishes a comprehensive pest control model using the Integrated Pest Man-agement(IPM). It deals with the pest control strategy of using chemical and biological control at fixed time and at different frequencies and the pest control strategy of the combination of the control at fixed time and the state-dependent control respectively. As for the control strat-egy of spraying pesticide at fixed time and releasing enemy, two different situations offer pest-eradication periodic solutions for the global asymptotic stability and the sufficient conditions for the enemy's survival. The times and period of spraying pesticide in the threshold, the number of the released enemy, and the significant effect the survival rate of pests and enemy and so on have on pest outbreak and eradication are analyzed numerically, and the optical systematic control period, times of spraying pesticide and the significance of pests' control of enemy are obtained. As for the comprehensive control strategy of the hybrid pest control, the effect enemy's hunting prowess have on pest outbreak is analyzed numerically. Then the relationship between the aver-age outbreak period of the hybrid control system and the parameter of the system is given and the key parameter affecting pest outbreak period considerably is obtained.Considering the lag phase and residual period after pesticides enter pests, pests' resistance to pesticides and other factors, Chapter 4 suggests using the pollutant discharge model to sim-ulate pesticide spray, and gives and introduces successfully the dose-response function to the comprehensive pest control model. It discusses the chemical control strategy to eradicate pests when enemies exist or do not exist respectively. When enemies exist, it discusses the following two different control strategies:(1)the frequency of spraying pesticides is higher than that of releasing enemy; (2)the frequency of releasing enemy is higher than that of spraying pesticides. As for different control strategies, the sufficient conditions for the periodic pest-eradication so-lution existence and local asymptotic stability are obtained. By using numerical simulation, we analyze the threshold sensitivity to the parameter, identify the major factors affecting pest con-trol and provide the guidance for the optical control strategy. Next, when the times of spraying pesticides or releasing enemy are different, it offers the spray and release period, spray dose and the effect the environment's getting toxin has on the critical condition of pest-eradication and concludes that pesticides have a significant effect on enemy. To curb pests' resistance to pesticides, we introduce the resistance evolution equation only to the pest control model of us-ing chemical control. To curb pests' resistance to pesticides, we put forward three strategies of changing pesticides according to different criteria and discuss the optical pesticide change option. We do research on the effect releasing enemy has on pest control to eventually reduce the times of spraying and changing pesticides when using the comprehensive chemical and bio-logical control.