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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.

Reviewer: E. Ahmed (Mansoura)

### 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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\textit{W. Liu} et al., J. Franklin Inst. 348, No. 6, 1114--1127 (2011; Zbl 1225.34055)

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### References:

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