Study On The Stability And Optimal Harvesting Problem Of The Three Species Prey-Predator System With Ratio

In recent years,the rapid development of mathematical biology promoted the development of fisheries,medicine,agriculture,forestry,bioinformatics,cell biology and many other fields.The population dynamics is one of the most classic and broad research field in mathematical biology.It has laid a solid foundation for the development of biological resources optimization management and integrated pest management,which provides a theoretical guidance for the optimal management of renewable resources.Study on the stability and protection of population resources of three species predatorPrey system based on ratio has profound practical significance.Because of many artificial factors affecting species capture,so the reasonable development and protection of population resources is particularly important.Therefore,this paper mainly focuses on the study of population dynamics behavior and optimal management of renewal resources.The main contents of research is:(1)We study the rate dependentn three species predator-prey model in this part.And the sufficient condition for the stability of the positive equilibrium point can be obtained by using the theory of differential equations,Routh-Hurwitz discriminant method and Lyapunov stability theorem.(2)We research a predator-prey system with B-D functional response in the case of double density constraints.Moreover,we discusses the Optimal acquisition strategy of the predator-prey system by using the stability theory of differential equations,Routh-Hurwitz method,Lyapunov stability theorem and Pontryagin's maximum principle.It provides some guidance for the sustainable development and management of the biological population.(3)In this part,we study a predator-prey model with taxation and Michaelis-Menten functional response.Based on the stability theory of differential equations,the sufficient conditions for the existence of positive equilibrium points and asymptotic stability are obtained by Routh-Hurwitz method and Lyapunov stability theorem.Finally,the optimal tax policy is studied by using the Pontryagin's maximum principle.The numerical simulation is carried out by using MATLAB to verify the correctness of the conclusion.