Application Of Impulse Differential Equation In Pest Management Model

The control of agricultural pests has always been a problem puzzling agricultural producers and scientific and technological workers.Since the human society entered the farming period,the control of agricultural pests has become the primary consideration in agricultural production.For the control measures of agricultural pests,there are roughly two kinds: chemical control and biological control.As a single control measure has its own shortcomings,scientists began to explore integrated pest control measures,that is,use chemical control and biological control at the same time,and scientifically coordinate the intensity and mode of use of the two,so as to reduce the harm of a single control measure to the ecological environment,and at the same time make agricultural production cost to the lowest.The work of this paper is to establish the SI model of pest control with impulse effect based on impulse differential equation,and apply the comparison theorem of impulse differential equation,Floquet theory and the definition of the persistence of impulse differential system to analyze the model qualitatively.It is divided into four parts: In the first part,the application prospect and significance of impulse differential equation in agricultural pest control are introduced,and the research status at home and abroad is summarized briefly.In the second part,based on the integrated pest control strategy,a fixed time pulse control model was established to discuss the uniform bounded nature of the model solutions,the conditions of the existence of the periodic solutions of pest extinction,and the conditions of the system persistence.Finally,the results were verified by numerical simulation.In the third part,based on the integrated pest control strategy,the pest control model with state feedback pulse control was established,the dynamic behavior of the subsystem was analyzed and the local asymptotic stability of the boundary periodic solution of the system was studied.Finally,the conclusion of biological significance was obtained by numerical simulation.In the fourth part,a pest management model with state feedback pulse control and fixed time pulse control was established based on integrated pest control measures,and the uniform boundedness of the system solution,the global asymptotic stability condition of the periodic solution of pest extinction,the condition of the system persistence and the condition of the existence of the periodic solution were discussed.Finally,the results were verified by numerical simulation,and a conclusion of biological significance was obtained by comparing the models established in the second and third parts.