Title of article :
Stability and bifurcation in a delayed predator–prey
system with Beddington–DeAngelis functional
response
Author/Authors :
Zhihua Liu، نويسنده , , Rong Yuan، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2004
Abstract :
We consider a delayed predator–prey system with Beddington–DeAngelis functional response.
The stability of the interior equilibrium will be studied by analyzing the associated characteristic
transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation
can occur as the delay τ crosses some critical values. The direction and stability of the Hopf
bifurcation are investigated by following the procedure of deriving normal form given by Faria and
Magalhães. An example is given and numerical simulations are performed to illustrate the obtained
results.
2004 Elsevier Inc. All rights reserved.
Keywords :
Hopf bifurcation , stability , Normal form , Time delay , Predator–prey system
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications