Establishment and analysis of a shared resource predator-prey model with harvest
In this paper,a shared resource predator-prey model with linear harvesting rate and Holling type Ⅱ functional response func-tion is established,and the existence and stability of the equilibria of the system are analyzed.There may exist the prey-free equilibri-um,the predator-free equilibrium,and the positive equilibrium in the system.Through qualitative analysis,we give the conditions that the prey-free equilibrium is stable,saddle,or saddle-node one,respectively,and find that the predator-free equilibrium always be sad-dle one.Furthermore,we obtain the conditions that the positive equilibrium is stable.Finally,some numerical simulations are carried out.It was found that different values of harvesting rate can change the stable state of the system.Hence,the optimal harvest for hu-man fishing can be obtained while ensuring ecological stability using theoretical analysis.
harvesting ratepredator-prey modelHolling type Ⅱ functional response functionequilibrium
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