Analysis And Amplitude Control Of Aphid Population Model With Weak Allee Effect Based On Washout Filter

Aphid populations are small sap sucking insects,they hinder the growth of crops by transporting some disease and feeding on the sap of the crops.Aphid populations do seriously harm to agriculture,while,they are also one of the most destructive pests on the earth.On the background of Aphid ecosystem,the corresponding model with delay is built by considering the effect of the natural environment on the aphid populations.Using the Hopf bifurcation theory,the model is analyzed.In order to reduce the harm of aphid populations to crops the model with washout filter is introduced to control aphid populations.The specific contents are as follows:1.The model with weak Allee effect is used to describe the growth of aphid populations.Considering the effect of the natural environment on the aphid populations,the corresponding delay model is built.The dynamic properties of the model and the conditions of Hopf bifurcation are obtained by the qualitative theory of differential equations and Hopf bifurcation theory.2.For the delay model of aphid populations with weak Allee effect,the corresponding model with washout filter-aided linear feedback control is built by releasing natural enemies populations.In order to avoid the critical period of crop growth,namely grouting period,the controller is designed to change the position of Hopf bifurcation.3.For the delay model of aphid populations with weak Allee effect,the corresponding model with washout filter-aided nonlinear feedback control is built by releasing natural enemies populations.In order to avoid touching the economic threshold of aphid populations,the controller is designed to change the limit cycle amplitude generated by Hopf bifurcation.4.For the delay model of aphid populations with weak Allee effect,the corresponding model with washout filter-aided linear and nonlinear feedback control is built by releasing natural enemies populations.The controller is designed not only to changes the position of Hopf bifurcation,but also to change the limit cycle amplitude generated by Hopf bifurcation.In this paper,three feedback controllers are designed to change the outbreak time and fluctuation amplitude of aphid populations,by introducing Washout filter.On the one hand,the paper widens application field of washout filter,on the other hand,it provides reference for the effective management of aphid populations.