The Qualitative Analysis And Optimization Impulsive Control Of Pest Population Models With Cusp Catastrophe

It is well known that crop production is the foundation of the national economy. Pest outbreaks are a catastrophe phenomenon that can do great harm to crops. It is necessary to control the pest with economic threshold. Under the background, it shows important theoretical significance and practical application value to analyze and control the pest population models with cusp catastrophe.According to the principles in ecology and economics in this paper, the models of pest population with cusp catastrophe are built up by means of revising Logistic model. Using the method of qualitative analysis of dynamic systems and the principle of optimization impulsive control, the models are analyzed and controlled which makes the pest populations reach the appropriate level. The main contents are as follows:Part I, on the basis of Logistic model, the model of pest populations with cusp catastrophe are proposed by studying for the growth of pest populations. The model is analyzed using the qualitative theory of differential equations and catastrophe theory, and the conditions of catastrophe are obtained. Finally, the simulations are carried to prove the results.The study may provide the theoretical foundation for pest forecast.Part II, based on the model of pest populations with cups catastrophe in Part I and the method of chemical control, the corresponding control model with impulsive effects is given.According to the principle of optimization impulsive control, the controller is designed to avoid the time which keeps the largest number of pest populations, and control the number of pest populations under the economic threshold. Finally, the simulations are carried to prove the results. The study may provide the foundation for pest control.Part III, based on the model of pest populations with cups catastrophe in Part I,considering the influence of environment on pest population, the pest population model with delay is proposed. The model is analyzed using the stability theory for applying the control in the model as a foundation.