Research And Analysis On Dynamics Of Mathematical Models For Biological Control Of Several Aphids

Crop aphid control has always been a complex ecological problem.Traditional chemical pest control techniques have led to many drawbacks such as reduced grain production and environmental pollution.The development of sustainable agriculture has accelerated research on biological control of aphids.In this paper,three mathematical models are established based on the biological control strategy of crop aphids,and the possible problems and solutions in the process of aphid biological control are comprehensively studied from the perspectives of dynamic analysis and numerical analysis.The main research contents are as follows:In the first chapter,the research background,significance,and current status of aphid biological control are mainly introduced,and some basic theoretical knowledge is provided.In the second chapter,a host-parasitoid-predator model based on ladybug pulse release is constructed.By adjusting the release amount and release time of ladybugs,long-term control and optimal control with limited time are studied respectively.For long-term control,we study the existence and stability of the periodic eradication solution of aphids,and obtain threshold conditions for the release amount and release period that ensure the ultimate extinction of the aphid population.For limited-time control,three different optimal pulse control problems are studied.Using time-scale transformation techniques and gradient-based optimization algorithms,we obtain the optimal release amount and release time for ladybugs.Furthermore,numerical analysis results show that in limited-time control,release time should have a higher priority than release amount.In the third chapter,a new generalized logistic aphid population biological control model is established based on ladybug pulse release,which has growth-stage structure.Because the capturing abilities of ladybugs at different stages differ,a piecewise discontinuous function is constructed to characterize the number of ladybugs in the environment under different release periods.The existence conditions of positive periodic solutions of the system are determined theoretically using the fixed-point theorem,and are confirmed numerically.Under different circumstances,the aphid population can be effectively controlled and eventually eradicated by increasing the release rate of ladybugs.In the forth chapter,a aphid biological control model using semi-continuous dynamic systems is constructed,which takes into account the impact of meteorological factors and state feedback pulse control.First,the dynamical properties of the uncontrolled system and the controlled system are studied,including the existence,uniqueness,and stability of equilibrium points and periodic solutions,and the attraction domain of the system.Then,numerical simulations are used to verify the theoretical results and analyze the effects of temperature,humidity,and predator release on the development of the two types of populations and the effectiveness of aphid biological control.The fifth chapter summarizes the full text and gives the prospect further.