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BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY
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- Journal:
- The ANZIAM Journal / Volume 57 / Issue 4 / April 2016
- Published online by Cambridge University Press:
- 12 May 2016, pp. 445-460
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- Article
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We consider a coupled, logistic predator–prey system with delay. Mainly, by choosing the delay time
${\it\tau}$ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time 
${\it\tau}$ passes some critical values. Based on the normal-form theory and the centre manifold theorem, we also derive formulae to obtain the direction, stability and the period of the bifurcating periodic solution at critical values of 
${\it\tau}$. Finally, numerical simulations are investigated to support our theoretical results.
