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.


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


Full Text: DOI


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