| Our country is a strong agricultural country and agriculture is the economic foundation of our country.The effect of pest control is a key factor of affecting agricultural development.Integrated pest management is developing rapidly,and chemical control is one of the important means.However,with the long-term and high-frequency use of chemical pesticides,the resistance of pests has also been developed,which has attracted the attention of many experts and scholars at home and abroad.In order to control the development of pesticide resistance effectively and achieve the purpose of pest control,experts and scholars from various countries have proposed many control strategies.And the commonly used strategy is to adopt other control methods,such as biological control,that is to put natural enemies while taking chemical control of pests.At the same time,the goal of pest control is not to eradicate pests,but to control their density below the economic injury level.That is,control measures are taken only when the pest population density reaches or exceeds the economic threshold.How to balance chemical control and biological control to achieve the best control strategy?This is a problem that the agricultural management department is very concerned about.Through the establishment of mathematical models and analysis of its dynamic behavior,it is helpful to provide decision-making basis for the agricultural management department.This article first establishes the prey-predator model without implementing pest control measures when the pest population density does not reach the economic threshold.And when the pest population density reached or exceeded the economic threshold,the prey-predator development model with the development of pesticide resistance under comprehensive control measures is implemented.By using the non-smooth Filippov system to combine the two types of models,a type of Filippov model for comprehensive pest control under the development of pesticide resistance is established.By analyzing the dynamic behavior of the model,we can study the key factors causing the development of drug resistance,which can help to propose the optimal control strategy.Firstly,through the use of ordinary differential equation stability and qualitative analysis,the existence and stability of the equilibrium for two subsystems of the Filippov model and all kinds of equilibrium of the Filippov system are studied in detail,and the results show that the model have the real and virtual equilibrium,boundary equilibrium,pseudo-equilibrium and tangent points.Secondly,using the Filippov convex combination and Utkin equivalent control method,the theoretical knowledge of the hybrid system,the sliding domains and the sliding dynamics of Filippov system are investigated,which show that the sliding segment of the Filippov system has a linear relationship with the resistance of pests,that is,as the pest resistance increases,the sliding area gradually decreases.Finally,through the method of numerical simulation,the sliding bifurcations of the filippov model are analyzed and studied,including boundary focus bifurcation,buckling bifurcation,grazing bifurcation and crossing bifurcation,and the results show that ? decreases significantly faster as ET or ? decreases.These complex sliding bifurcations reveal that we can control the relationship between ET and sprayed pesticides and released the number of natural enemies to achieve the purpose of integrated pest management.It is found that the parameter economic threshold ET and the constant number of natural enemies ? play an important role in affecting the dynamic behavior of the system.That is,the smaller of controlling ET,the quicker of pesticide resistance increasing,and the smaller of releasing the number of natural enemies,the quicker of pesticide resistance increasing.Thus,we can take the method of releasing the natural enemies after spraying certain pesticides,which can help to reduce the pest resistance and reduce the farmer's crop losses. |
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