Study On The Integrated Pest Management Model Based On Interval State Dependent Feedback Control

Pest management is an important component of agricultural sustainable development.Traditional pest management includes two methods: chemical control and biological control.Integrated pest management is the comprehensive utilization of agricultural,biological,chemical and physical methods to control pest concentration that makes its control be in a reasonable economic threshold.In the past,the control strategy based on state feedback is assumed that chemical control and biological control were taken at the same pest density level,but considering the pest management in practice,biological control was generally earlier than chemical control,in order to better reflect the actual pest management process,we proposed a pest control strategy based on interval state feedback control,i.e.,when the concentration of the pest reaches the first monitoring concentration,we adopt biological control methods;once the pest concentration reaches or exceeds the second monitoring concentrations,we adopt a chemical control method.First,we established a class of Gompertz predator-prey model based on interval state feedback control.The existence of periodic solutions of the system is analyzed by means of Poincaré theorem and successor function method.At the same time,Bendixson theory is used to analyze the stability of periodic solution.Finally,the numerical simulation of the established model is carried out by using Matlab software to verify the accuracy of theoretical analysis.Secondly,two types of x~k type predator-prey model based on interval state feedback control were established.The first type is a x~k type Lotka-Volterra predator-prey model with interval adjustable control level.Application of Jacobian matrix proved the global asymptotic stability of solutions for continuous systems.The application of Dulac function proved the nonexistence of limit cycles.The existence and stability of the periodic solution of the control system were analyzed by means of Poincaré theorem and successor function method.At the same time,the pest control concentration was taken as the optimization variable,and the target function of control cost was optimized.The second type is a x~k type Gompertz predator-prey model based on interval state feedback control.The global asymptotic stability of the solution of the continuous system was proved by using the characteristic root method and the Bendixson-Dulac theorem.Then,the existence and stability of the periodic solution of the control system were analyzed by using the Poincaré theorem and the successor function method.Finally,the numerical simulation of the established model is carried out by using Matlab software to verify the accuracy of theoretical analysis.