Analysis Of The Optimal Harvesting Strategy For Development Of The Predator - Prey System

With the rapid development of social economy, the exploitation and management of biospecies resource are more and more concerned. The ecological benefits and economic benefits are regarded as the main principle of exploitation, which make it possible for people to use biospecies resource durativity. In recent years, the problem of exploitation and management of biospecies resource is a hot issue, which is researched by many scholars, and some important yield is obtained.The optimal harvesting policy on a developed predator-prey system is analyzed in this paper, and several aspects are stressed:1. The situation of a prey population with constant rate stocking is discussed. The sufficient conditions for existence and uniqueness of limit cycles are obtained in the predator-prey system. At the same time, the ecological meaning is explained.2. The situation of a prey population with the linear harvesting is discussed. In this predator-prey system, the stability of the positive equilibrium and the existence of Hopf bifurcation are analyzed. Through the analysis of the half open system, a best optimal harvesting policy of the open system is obtained, which is regard as the goal of maximum sustainable gain. At the same time, a reasonable taxation policy is given by the Gordon's theory in economy. Biological resources got effectively protected.3. The situation of a prey population with the optimal harvesting is discussed. In this predator-prey system, the locally and globally asymptotically stable for positive equilibrium point is analyzed. By using Pontryagin's maximum principle, a optimal harvesting policy and a reasonable taxation policy are obtained. This paper is useful for protection of species group resources.