Mathematical Simulation Study On Pest Control With Transient And Non-transient Impulsive Effects

Pest control is an important part of agricultural production.In recent years,the occurrence rate of diseases and pests is high in China,which has a significant impact on agricultural production.Chemical control(spraying insecticides)and biological control(releasing natural enemies)are the most commonly methods.In this paper,it is considered that pesticides may have a non-transient residual effect on pests and natural enemies while killing amounts of pests and natural enemies instantly after spraying.In addition,after the spraying of pesticides,the predation rate and conversion rate of natural enemies are different under the influence of pesticides.The pest control model with transient and non-transient impulsive effects is established,and the dynamic properties of the model are analyzed systematically.In the first chapter,some basic concepts and theorems needed for our research are provided.In the second chapter,a class of pest control model with transient and non-transient impulsive effects is established by considering the spraying and releasing of natural enemies at different fixed times and the non-transient residual effects of pesticides.Firstly,the sufficient condition for the existence of periodic solutions of pest extinction and the global asymptotic stability of pest extinction threshold are obtained by using the comparison theorem of impulse differential equations and the methods of analysis.Then,the relationship between the extinction threshold and the time of spraying pesticides,the amount of natural enemies released,the non-transient killing rate of pesticides and the pest control cycle are analyzed by numerical simulation.In the third chapter,on the basis of the second chapter,the control strategy with different frequencies of spraying pesticides and releasing natural enemies is introduced.In the first place,pest control model with transient and non-transient impulsive effects with different frequencies is established.A sufficient condition for the global asymptotic stability of the extinction periodic solution is obtained under the assumption that spraying pesticides is more frequent than releasing natural enemies.The next,the dynamic complexity of the model is studied systematically.The numerical simulation results show that there will appear from period-doubling branching?chaos?period-branching?chaos as the pulse control period increases;And with the increase of the amounts of natural enemies released,the complex dynamic behavior of the system will appear,which is period-doubling bifurcation?chaos? backward period-doubling.At the same time,multiple attractors coexist in the system.For a set of parameters,the stable positive periodic solution or extinction of the pest population tends to be depends on the initial value.After that,the influence of the key parameters on the extinction threshold of pests is analyzed.The results suggest that there is an optimal time to spray pesticides and it is not the more frequent spraying of pesticides that leads to better pest control.In the end,in order to reduce the negative impact of overuse of pesticides on the environment,we consider that pesticides should be applied only when the pest population reaches a certain economic threshold.A state-dependence pest control model with transient and non-transient impulsive effects is established.The numerical simulation results shows that the number of pesticides used depended on the initial population density,the amount of natural enemies released and the period of releasing natural enemies.This control strategy is ecologically and economically more effective.