Hopf bifurcation analysis for a ratio-dependent predator-prey system involving two delays

H. Merdan

Abstract


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.

doi:10.1017/S1446181114000054

Keywords


Hopf bifurcation, delay differential equation, time delay, stability, periodic solutions, population dynamics



DOI: http://dx.doi.org/10.21914/anziamj.v55i0.6271



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.