Establishment,Analysis And Control For Agricultural Plant Diseases And Pest Model

In agricultural production,the plant diseases and insect pests have always been a basic problem that plagued the growth of the crops.In fact,the chemicals are overused to prevent and control the plant diseases and insect pests.With the appearing of the problems for the ecological,economic and social,scientific management of agricultural plant diseases and insect pests has become one of the urgent problems to be solved.Currently,with the rapid development of computer science and computational mathematics,a set of effective management methods for agricultural plant diseases and insect pests are proposed as follows:Firstly,the biodynamic models are established to describe the occurrence and development of the plant diseases and insect pests.Secondly,using dynamic system theory to analyze the complex dynamic behaviors of the plant diseases and insect pests and reveal the ecological mechanism of its outbreak.Finally,in order to effectively manage agricultural plant diseases and insect pests,proper controllers are designed to keep the density of the pathogenic bacteria population or the aphid population at a level that does not affect the growth of the crops.Therefore,based on the population growth models,the differential equation model,impulsive differential equation model and singular system model of the plant diseases and insect pests are established respectively in this paper.The analysis methods and controller design problems are discussed according to the different models,and new ideas and new methods of establishment,analysis and control for the plant diseases and insect pests(botrytis cinerea and aphids disease)model are formed.The main research can be briefly described as follows:1.Based on the interaction between the pathogenic bacteria population of the botrytis cinerea and the crop population in greenhouse,a differential equation model is proposed.According to the actual management measures,such as removing infected plant and leaves,and spraying bactericide,the corresponding control model is established.Using the qualitative theory of the differential equation,the global stability of the model is analyzed and the occurrence and development of the botrytis cinerea of the vegetables and fruits in greenhouse are predicted.According to the harm's degree of the pathogenic bacteria population of the botrytis cinerea to the vegetables and fruits population,the T-S fuzzy models are built up.The controllers are designed by using T-S fuzzy control theory to keep the density of pathogenic bacteria population of the botrytis cinerea under the level which has not impacted on the growth of the vegetables and fruits population.Finally,based on actual issues arising from management of the strawberry aphid,some computer simulations are carried out to prove the results and verify the effectiveness of the controllers.2.Based on the predator-prey relationship between the aphid pests population and the natural enemy population,a non-smooth population model with impulsive effect is proposed,which combines discontinuity and non-smoothness.According to the qualitative theory of the differential equations,the global analysis of the model is discussed.The independent characteristics of the model at non-smooth equilibrium points are specially pointed out.Using the geometric theory of semicontinuous dynamic system,the existence conditions of Order one periodic solution are obtained and the stability of Order one periodic solution is analyzed.Management measures such as spraying bactericide and releasing natural enemy are taken,the impulsive controllers are designed to make the aphid pests population stay at the refuge level.Finally,some computer simulations are carried out to prove the correctness of the theoretical analysis and the effectiveness of the controllers.3.Based on the interaction between the aphid pests population and the variables for morphological characteristics of the fruit trees,the algebraic equation which describes the constrained condition is derived from the differential equations which describe the dynamic growth of the population,then a singular system model is proposed.The qualitative theory of the differential equations is extended to the singular system model,and the ecological explanations of the aphid pests population outbreak are given.Variable structure controller and T-S fuzzy controller are designed to stabilize the aphid pests population to the target state as quickly as possible.Finally,some computer simulations are carried out to prove the correctness of the conclusions and show the application effects of the controllers in the orchard ecosystem.4.Based on the catastrophe model of the aphid pests population,considering the change of the parameter related to the natural enemy population and the impact on the aphid population,the differential equation is derived from the algebraic equation which describes the fold catastrophe manifold,then a singular system model of the aphid ecosystems is proposed.Using geometric analysis method,the complex dynamic behaviors of the singular system model and the corresponding biological significances are discussed.According to the existence conditions of the impasse points,the relationship between the sudden change of the aphid pests population and the impulsive behavior of the singular system is explored.Two controllers are designed to manage the aphid pests and some computer simulations are carried out to prove the results.Finally,based on the existing data,the experiments are designed to collect data,then the model checking scheme is given by the hypothesis significance testing.Finally,concluding remarks are given.Some problems existing in the application of the above modeling,analysis and control methods in the actual agricultural plant diseases and insect pest management are pointed out and the corresponding improvement schemes are proposed.Furthermore,the prospects of the further study are given.