The Optimal Harvest Strategies For Several Types Of Predator-Prey System

There are huge significances for rational exploitation of the biotic population in ecosystem, some extensive and intensive studies are done by many scholars. This article would study on two types of discrete time predator-prey systems aiming at maximizing their profits and capture by using differential methods, quadratic function theory and Gordon theory respectively. Finally, we obtain captured strategy of the simultaneous capture and separate acquisition.To the problem of harvest strategies for a discrete time predator-prey system which have density dependence, we consider the situation of simultaneous capture. We give the locally stable conditions of non-negtive points by applying the theory of differential equation. Under the premise of maintaining sustainable capture to obtain maximum economic benefits or maximum amount of capture, we get appropriate capturing tactics under different capturing efforts. Then we discuss the independent capturing of predator population. Considering the influence of flexible price and variable cost to capturing efforts, we redefine the point of economic equilibrium and analyse the stability of the point of economic equilibrium by applying Gordon theory. We prove that the point of economic equilibrium tends to zero as the growth of price and the reduction of cost, which could lead to the extinction of population. The government should levy taxes in order to gain sustainable balanced capture. We revise the original condition of economic equilibrium and get the appropriate taxes and the optimal harvest strategies finally.We do a research on a predator-prey system which has functional response function. Firstly, we discuss the situation of simultaneous capture by using the theory of differential methods to get locally stable conditions of non-negtive points. Under the premise of sustainable capture, we get the optimal harvest strategies aiming for maximum economic benefits or amount of capturing. Secondly, in the case of independent capture, we discuss the stability of the point of economic equilibrium. By applying Gordon theory under the condition of flexible price and variable cost, we prove the extinction of population as the growth of price and the reduction of cost. We establish a new condition of economic equilibrium through the method of taxation levied by the government. We get the appropriate taxes to gain maximum capture and give the optimal harvest strategies finally.