| Pests are one of the many factors affecting crop growth and have serious destructive effects on the crops,especially in the critical period of the growth.The outbreak of pest populations may lead to the substantial reduction of crop production.On the background of the pest populations,the model under the influence of enemy populations and the corresponding management model with washout filter are established based on the population model with Holling-III functional response;The analysis and synthesis are finished from the perspectives of static catastrophe and dynamic catastrophe.The main contents are as follows:1.Based on the model of pest populations with Holling-III functional response,the catastrophe analysis of the model is conducted using the quantitative and qualitative theory of ordinary differential equations,which shows the ecological mechanism behind them.2.Considering the influence of enemy population in natural environment on pest population,a pest population model under the threat of natural enemies is established.Firstly,the equilibrium point and stability of the model are qualitatively analyzed;Secondly,the sufficient condition for the model to generate Hopf bifurcation is given by using the bifurcation theory.3.Based on the pest population model under the threat of natural enemies,considering the similarity between the structure of enemy populations in natural environment and washout filter,firstly,the management model of pest populations with washout filter is established.Secondly,In order to avoid the critical period of crop growth,the linear feedback controller is used to change the position of Hopf bifurcation.Finally,the limit cycle amplitude is reduced to manage the outbreak of pest populations within its economic threshold by the nonlinear feedback control.On the one hand,the thesis provides the theoretical basis for the prediction and management of pest populations;On the other hand,it broadens the application field of washout filter. |
