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**Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response.**
*(English)*
Zbl 1051.34060

Authors’ abstract: We consider a delayed predator-prey system with Beddington–DeAngelis functional response. The stability of the interior equilibrium is studied by analyzing the associated characteristic transcendental equation. By choosing the delay \(\tau\) as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay \(\tau\) crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving a normal form given by Faria and Magalhaes. An example is given and numerical simulations are performed to illustrate the obtained results.

Reviewer: E. Ahmed (Mansoura)

### MSC:

34K18 | Bifurcation theory of functional-differential equations |

92D25 | Population dynamics (general) |

34K20 | Stability theory of functional-differential equations |

### Keywords:

Beddington-DeAngelis predator-prey system; time delay; stability; Hopf bifurcation; normal form
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\textit{Z. Liu} and \textit{R. Yuan}, J. Math. Anal. Appl. 296, No. 2, 521--537 (2004; Zbl 1051.34060)

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### References:

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