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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.

34C60Qualitative investigation and simulation of models (ODE)
34C23Bifurcation (ODE)
92D25Population dynamics (general)
34A09Implicit equations, differential-algebraic equations
Full Text: DOI
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