Harvesting In Single Population With Dynamic Price

With the increasing demand for biological resources in human society,it is very important to capture or utilize biological resources reasonably.Among them,the sustainable development of biological resources and the benefits of developers is a natural problem.From the existing literature,in most studies,the price in income is often treated as a constant.As we all know,price are affected by supply and demand.In fact,supply and demand are in the opposite direction and in the same direction as price,respectively.In this paper,based on the classical open self-feedback capture model with constant price and based on the price theory,a new single harvesting model with dynamic price is established.Obviously,this idea is also suitable for a variety of group models.In this paper,we only give a specific dynamic analysis of the harvesting of Logistic and Gompertz growth models.The main work as follows:(1)From the point of view of single population biology and economics,the classical open self-feedback harvesting model is introduced.After explaining that price is the key factor of economic benefit,a new harvesting model with dynamic price is established according to the price theory.(2)The harvesting problem of Logistic growth model with dynamic price is studied.Firstly,the equilibrium is calculated and proved theoretically that the equilibrium is locally asymptotically stable.Secondly,the equilibrium surface is drawn for dynamic analysis.Then,the numerical simulation of the specific parameters is given to verify the correctness of the theory,and explanation is given from the point of view of bioeconomics.Finally,the conclusion is drawn and the suggestions are given.(3)The harvesting problem of Gompertz growth model with dynamic price is studied.In order to be intuitive,this model takes the price as the cross section drawing to carry on the correlation analysis.First of all,the equilibrium is calculated and proved from the theoretical point of view that the equilibrium is locally asymptotically stable.Next,the dynamic analysis is carried out with the equilibrium price as the cross section.Secondly,Matlab is used to draw the path diagram which approaches the equilibrium with the equilibrium price and the constant price,and the corresponding explanation is given.Finally,the necessary conditions for the optimal strategy are given by using the Pontryagain maximum principle in the optimal control theory.