Analyses On Several Non-smooth Dynamic Models Of Pest Management

Pest management is a complex ecological management system,which contains many factors,which need us to make a systematic study with the help of the establishment of a dynamic model,theoretical accurate analysis,and computer numerical simulation,so as to make the best control strategy.In this paper,based on the impulsive differential equation,considering the dynamic development of pest population,the persistent action mechanism of pesticides,and dynamic evolution of pest resistance,hybrid non-smooth pest control dynamic models are established from different angles by using a single population stage structure pest,two species pest-natural enemy and two species pest-natural enemy epidemic models,and the dynamic properties of the models are studied,the key factors affecting pest control are analyzed to give the best strategies for pest control.In the second chapter,it is assumed that the pest population has a stage structure,which is divided into two stages: larvae and adults,and the adults-only lay eggs at a fixed time every year.Considering that pesticides are sprayed only for a period of time after the growth of adults,and the mortality and conversion rate of pests are different before and after spraying pesticides,the subsection negative exponential function and pollution emission model are used to simulate the pesticide action mode respectively to establish a class of growth pulse pest management switching model based on pesticide action function.Adapting Jury criterion and theoretical analysis to obtain the threshold conditions of pest population extinction or population persistence.The numerical simulation results show that the system has complex dynamic properties,and make a further analysis of the key parameters affecting the threshold of pest population extinction or persistence and the optimal spraying times of pesticides in a pulse growth cycle.In the third chapter,firstly,considering that pesticides kill pests and natural enemies in a large amount at the instant of spraying,they still have a non-instantaneous residual effect on pests and natural enemies,and the conversion rates of natural enemies to pests are different before and after spraying pesticides,and considering the limited natural enemy resources,assuming that pesticides are sprayed more frequently than natural enemies are released,a generalized switching model of integrated pest management with instantaneous and non-instantaneous pulse effects is established.By using the Floquet theory and analysis method,the sufficient conditions of local asymptotic stability and global attraction of periodic solutions of pest extinction are obtained,and the relationship between local and global asymptotic stability is discussed by respectively taking linear and Holling II functional response capture functions as examples.When the capture function is linear,local asymptotic stability means global asymptotic stability.When the capture function is Holling II functional response capture function,the local asymptotic stability of the periodic solution of pest extinction can not guarantee its global asymptotic stability.Further analysis showed that the system has complex dynamic phenomena.Through numerical simulation,the influence of key factors on the threshold of pest extinction is analyzed.The results show that the threshold is not a monotonic function of the control period of natural enemies,and not that the more frequent pesticide spraying is,the better the pest control will be.Secondly,in order to reduce the negative impact of excessive use of pesticides on the environment,considering that pesticides are sprayed only when the population of pests reaches a certain economic threshold,a state-dependent pest management switching model with instantaneous and non-instantaneous impulse action is established.The numerical simulation results show that the number of pesticides used depends on the initial population density,the number of natural enemies released,the period of natural enemies released,and the instantaneous killing rate of pests and natural enemies by pesticides.This control strategy is more effective from ecological and economic perspectives.In the fourth chapter,it is assumed that pests can infect each other,and the pest population is divided into susceptible and infected pests,and only susceptible pests can cause harm to crops.Firstly,considering that the susceptible pests will produce resistance after repeated use of pesticides,we make use of pollution emission model to simulate the action mode of pesticides,deduce the development equation of resistance of susceptible pests,and discuss the effects of spraying dose of pesticides and absorption rate of susceptible pests on the equation.Secondly,considering the integrated pest management strategy of spraying pesticides and releasing infected pests and natural enemies at different frequencies,a non-smooth dynamic model of integrated pest management with resistance development is established and studied.Through numerical simulation,it is found that it does not show the higher the spraying dose of pesticides,the better the control of susceptible pests,and also not that the more frequent the spraying of pesticides,the better the control of susceptible pests.There is an optimal spraying frequency in a biological control cycle.Due to the development of resistance,susceptible pests will eventually break out.Finally,we put forward pest control strategies aimed at eradicating susceptible pests.From the perspective of chemical control,we give pesticide rotation strategies,including strong and weak rotation strategies.From the perspective of biological control,we adopt pulse elastic and continuous release of infected pests.Based on the extinction threshold of susceptible pests,we obtain analytical expressions of the release amount of infected pests that make susceptible pests extinct.The model established in this paper puts forward some new thinking methods and ideas for pest control,and the main conclusions obtained can provide the basis for the agricultural departments to design the optimal pest control strategies.