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BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY

Published online by Cambridge University Press:  12 May 2016

CANAN ÇELİK Open the ORCID record for CANAN ÇELİK [Opens in a new window]  and
GÖKÇEN ÇEKİÇ Open the ORCID record for GÖKÇEN ÇEKİÇ [Opens in a new window]
CANAN ÇELİK
Affiliation:
Bahcesehir University, Faculty of Engineering and Natural Sciences, Ciragan Cad., Besiktas, 34353 Istanbul, Turkey email canan.celik@eng.bahcesehir.edu.tr
GÖKÇEN ÇEKİÇ*
Affiliation:
Istanbul University, Department of Mathematics, Vezneciler, 34134 Istanbul, Turkey email gokcen.cekic@gmail.com
*
✉ gokcen.cekic@gmail.com
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Abstract

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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.

Keywords

predator–prey systemdelayed logistic differential equationHopf bifurcationstability

MSC classification

Primary: 92D25: Population dynamics (general)

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 4 , April 2016 , pp. 445 - 460
Copyright
© 2016 Australian Mathematical Society 

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