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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.

##### MSC:
 34K18 Bifurcation theory of functional differential equations 92D25 Population dynamics (general) 34K20 Stability theory of functional-differential equations
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##### References:
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