Amplitude Control Of Aphid Populations Model With An Allee Effect Based On Washout Filter

Aphids are one of pests worldwide and show the characters such as high population density and long-time damage.Aphids do damage to the crops by feeding on plant sap and transmitting virus.If the measures are not taken as soon as possible,aphids will cause serious losses to agriculture production.On the basis of the above,some models are built on the study background of aphid populations.The models are analyzed using Hopf bifurcation theory.The corresponding controllers with washout filter are designed to avoid the outbreak of aphid populations in critical period of crop growth.The specific contents of the paper are as follows:Part I For a model of aphid population with an Allee effect,the corresponding delayed model is built up.And then the model are analyzed by the qualitative theory of differential equations.Lastly,the critical value of Hopf bifurcation is determined and the amplitude of limit cycle obtained using Hopf bifurcation theory.Part II For a delayed model of aphid populations with an Allee effect,the enemy populations are introduced to build the corresponding control model with washout filter.And then the linear controller is designed to avoid the outbreak of aphid populations during grain filling stage of crops.Part III For a delayed model of aphid populations with an Allee effect,the enemy populations are introduced to build the corresponding control model with washout filter.And then the nonlinear controller is designed to make the density of aphid populations below the economic threshold and reduce the harm of aphid populations to crops.Part IV Based on the aphid populations model with an Allee effect,the corresponding control model is built.Combining linear feedback with nonlinear feedback,the controller with washout filter is designed not only to change the starting time of aphid populations fluctuation but also to reduce corresponding amplitude.In this paper,the amplitude control is applied in the study of the dynamics of aphid populations for the first time,which provides a reference for the effective management of aphid populations.