Hopf bifurcation for a predator-prey biological economic system with Holling type II functional response.(English)Zbl 1225.34055

A biological economic system which considers a prey-predator system with Holling type II functional response and harvesting on the prey is proposed. The model is described by differential-algebraic equations. By using the theory of differential-algebraic systems and the theory of Hopf bifurcations, the Hopf bifurcation of the proposed system is investigated. The economic profit is chosen as a positive bifurcation parameter here. It is found that Hopf bifurcation occurs as the economic profit increases beyond a certain threshold. Numerical simulations are carried out to demonstrate the effectiveness of our results. Some interesting open problems are given.

MSC:

 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C23 Bifurcation theory for ordinary differential equations 92D25 Population dynamics (general) 34A09 Implicit ordinary differential equations, differential-algebraic equations 92D40 Ecology

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