Study On The Effect Of Harvesting For Three Kind Of Population Dynamic Systems

This paper consists of three parts:Firstly, we propose a Leslie-Gower predator-prey model incorporating harvesting.By constructing a suitable Lyapunov function, we show that the unique positiveequilibrium of the system is globally stable, that is say, for this ecosystem, suitableharvesting has no influence on the persistent property of the system. The economicprofit is considered for the practical significance, and sufficient conditions for thepresence of bionomic equilibrium are given. Then, the optimal harvesting policy isobtained by using Pontryagin’s maximal principle.Secondly, a two-species competition system with toxic substance and harvestingis proposed and studied. After we give the explicit expression of the solutions of thesystem, the effect of harvesting on two species is investigated. The sufficientconditions which ensure the permanence or extinction of the species are obtained.After that, the effect of harvesting to economic profit is studied, and the captureefforts of two species are investigated in order to obtain the maximum economicprofit.Finally, we study a two-species competition system with toxic substance andnon-selective harvesting. We first obtain a set of sufficient conditions which ensuresystem admits unique internal equilibrium. After that, by constructing the suitableLyapunov functions, sufficient conditions which ensure the global stability of theboundary equilibriums and the internal equilibrium are obtained. The results improveand complement the corresponding results of T. K. Kar and K. S. Chaudhuri[61].