Analysis Of The Optimal Harvesting Strategy Of The Nonautonomous Predator-Prey Diffusion Model Analysis Of The Optimal Harvesting Strategy Of The Nonautonomous Predator-Prey Diffusion Model

With the rapid development of society and economy,the rational development and utilization of resources is not only related to the sustainable survival of the population,but also related to the sustainable development of society.In the process of utilization,if the ecological and economic benefits can be organically combined,then the population resources can be used by humans for a longer period of time.In recent years,the development and management of biological population resources has become a hot topic for scholars to discuss and study.In 2014,A.Moussaoui and others put forward a dynamic model of predator-prey under the influence of water level.It is of theoretical and practical significance to discuss the optimal harvesting strategy of the model under the capture conditions in combination with the actual needs of life.The full text is divided into three chapters:The first chapter,as preparation knowledge,gives the research background of this article,introduces constant coefficient harvesting model,variable coefficient harvesting model,diffusion harvesting model,and quasi-linear background knowledge.It also proposes the research content of this article and gives the relevant Theory,including the basic theory of the reaction-diffusion equations and the principle of variational method.The second and third chapters are about the optimal harvesting strategy of population model proposed by A.Moussaoui et al.The harvest of population biological resources is closely related to the development of human society.Therefore,the rational development and utilization of population biological resources has become an important research topic.There are many scholars,but the model they studied is more ideal.It is aimed at the continuous development of resources,and the population is evenly distributed in space,that is,the population is only related to time,and has nothing to do with the spatial location of the population.Based on the above reasons,the second chapter studies the existence and uniqueness of the solution of the population model proposed by A.Moussaoui et al.In the non autonomous form by using the upper and lower solution theory of the partial differential equation,and gives the corresponding optimal harvesting strategy according to the variational method.Finally,the numerical simulation of the existence and uniqueness of the solution of the nonautonomous diffusion model is given by using MATLAB.In recent years,there are many researches on population model,and thediscussion of related models is almost semi-linear.However,many phenomena can not be explained by semi-linear,so it is necessary to consider the quasi linear method.Therefore,in Chapter 3,based on Chapter 2,we continue to explore and discuss a kind of nonautonomous quasi linear predator-prey model with catch term.First,the upper and lower solutions of the model are constructed by using the upper and lower solution theory of the quasilinear partial differential equation with capture term,and the existence of the solution is proved.Then,the sufficient conditions for the existence and uniqueness of the solution are found by using the properties of the upper and lower solutions and the mixed quasi monotone.Then,the optimal capture quantity of the model is given by using the variational method.At the end of the paper,the main literature referenced in the research of this paper is given.