Lotka-volterra Predator - Prey Systems With Optimal Capture Problems

Reasonable utilizing of biological resource has direct relationship to sustainable development and economic revenue. It has biological and economic significance, so that it subject to scholar's consideration and they have a deep research.In the paper, we propose several different harvesting patterns, introduce price and cost factor and employ qualitative analysis method to the Lotka-Voterra prey-predator system with density constraint and without density constraint. We choose the maximum net rent as the management objective so as to get the optimal harvesting policy and have stronger directive meaning to real-life.The paper is organized as follows:In chapter 2, we give out models of lotka-VoIterra prey-predator system without that density constraint and get the optimal harvesting policy that takes the maximum net rent as management purpose, when harvesting ability are limited or unlimited. In section 2.1, we talked about the model of system in which two species are harvested respectively. In section 2.2, we talked about the model of system in which two species are simultaneously harvested and the harvesting tools are fixed. The section 2.3 concentrates on the model in which the two species are harvested simultaneously and the tools can be adjusted.In chapter 3, we give out Lotka-Volterra prey-predator model with density constraint and get the optimal harvesting policy that takes the maximum net rent as management purpose, when harvesting ability are limited or unlimited. In the first three sections we discuss the case and another case in which only predator species is exploited. Section 3.3 will take care about the model in which the two species are harvested respectively, and the last two sections are for the case in which the two species are harvested simultaneously, when tools are fixed and the case in which tools are adjustable respectively.