Qualitative Analysis And Catastrophe Control Of Aphid Populations Model Based On Allee Effects

Aphid populations are one of the most destructive pest.They clearly exhibits characteristics such as small body size,adequate number and highly reproductive,which leads to the large-scale outbreak of aphid populations frequently.If the aphid populations are not prevented timely,they can cause severe damage for crops and heavy economic losses.However,Allee effects models are usually used to describe the outbreak of populations.Under the background of aphid population ecosystems,the environmental impact model with delay is built by means of Allee effect models.The model is analyzed using the qualitative theory of differential equation.And the controllers with Washout filter are designed to reduce the density of aphid populations to the level that does not harm to the growth of crops,the specific contents are divided into two parts as follows.The first is model analysis:Considering the effect of environmental factors(such as meteorology,natural enemies,etc.)on the aphid populations,the corresponding model with delay effect is established based on the aphid population models with Allee effects.Using the qualitative theory of differential equations,the comprehensive and detailed geometric analysis are studied,and the dynamic changes of aphid populations affected by environmental factors are obtained.On the basis of the above,sufficient conditions for the occurrence of Hopf bifurcation are obtained.And then some simulations are carried to prove the correctness of the theoretical results.In theory,the study reveals the ecological mechanism of the aphid populations outbreak,which lays the foundation for the further application of the qualitative theory of differential equations in ecology.The second is model control:Based on the catastrophe phenomenon of aphid populations,the corresponding control model with Washout filter is constructed by considering the effect of enemy populations on aphid populations.After a linear feedback is used to determine the position of the catastrophe control,the corresponding nonlinear feedback controller with Washout filter is designed to eliminate the phenomenon outbreak of aphid populations.Some simulations are carried to show the effectiveness of controllers,The study expands the application field of catastrophe control.Completion of this paper actualizes the preliminary combination of catastrophe control theory,ecology and mathematics.