Stability and Hopf bifurcation analysis of a prey-predator system with two delays.

*(English)*Zbl 1198.34144Summary: We have considered a prey-predator model with Beddington-DeAngelis functional response and selective harvesting of predator species. Two delays appear in this model to describe the time that juveniles take to mature. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form method and the center manifold theory. Numerical simulation results are given to support the theoretical predictions.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:

34K18 | Bifurcation theory of functional-differential equations |

92D25 | Population dynamics (general) |

34K20 | Stability theory of functional-differential equations |

37N25 | Dynamical systems in biology |

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\textit{K. Li} and \textit{J. Wei}, Chaos Solitons Fractals 42, No. 5, 2606--2613 (2009; Zbl 1198.34144)

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