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Article

BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY

  • CANAN ÇELİK (a1) and GÖKÇEN ÇEKİÇ (a2)
Abstract

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.

Copyright
© 2016 Australian Mathematical Society 
Corresponding author
✉ gokcen.cekic@gmail.com
References
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