Bifurcation analysis of a logistic predator-prey system with delay


Celik C. , Cekic G.

ANZIAM Journal, vol.57, no.4, pp.445-460, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1017/s1446181116000055
  • Journal Name: ANZIAM Journal
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.445-460

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.