Bifurcation analysis of a logistic predator–prey system with delay

Canan Celik, Gokcen Cekic

Abstract


We consider a coupled, logistic predator–prey system with delay. Mainly, by choosing the delay time \(\tau \) as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time \(\tau \) 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 \(\tau \). Finally, numerical simulations are investigated to support our theoretical results.

doi:10.1017/S1446181116000055

Keywords


predator–prey system; delayed logistic differential equation; Hopf bifurcation; stability



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.9441



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