Study On Dynamics Of Three Kinds Of Predator-prey Dynamic Systems

This paper considers the dynamics of three kinds of predator-prey dynamic systems and studies the system from both theoretical and numerical aspects.The main research contents are as follows:The first chapter gives the research background and development status of the subject,as well as relevant definitions and lemmas,which provides a theoretical basis for the discussion of the following chapters.In chapter 2,a class of predator-prey dynamic system is constructed by introducing proportional capture and capture intensity.The theoretical work mainly focuses on the existence and stability of equilibrium point,the non-existence of limit cycle,the existence of ecological economic equilibrium point and the corresponding optimal capture intensity.The feasibility of theoretical work is verified by numerical simulation.In chapter 3,a class of phytoplankton-zooplankton dynamic system with optimal taxation measures is constructed by taxing the capture population(zooplankton)of unit biomass.Firstly,the existence and stability of the equilibrium point are analyzed.Secondly,the optimalsolution to the optimal tax revenue is obtained according to the Pontryagin maximum principle,and the tax revenue value that maximizes the discounted social income value is obtained.Finally,the feasibility and effectiveness of the theoretical results are verified by the numerical simulation.In chapter 4,a class of predator-prey impulse control dynamic system with steady release is established,the boundedness of the arbitrary solution of the system and the local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution are analyzed,the corresponding critical conditions are derived,and the threshold conditions for the system to maintain the long-term survival of the biological population are given.