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HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS

Published online by Cambridge University Press:  05 June 2014

E. KARAOGLU
Affiliation:
TOBB University of Economics and Technology, Faculty of Arts and Sciences, Department of Mathematics, Söğütözü 06530, Ankara, Turkey email ekaraoglu@etu.edu.tr, merdan@etu.edu.tr
H. MERDAN*
Affiliation:
TOBB University of Economics and Technology, Faculty of Arts and Sciences, Department of Mathematics, Söğütözü 06530, Ankara, Turkey email ekaraoglu@etu.edu.tr, merdan@etu.edu.tr
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Abstract

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The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Society 

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