Bifurcation analysis of a logistic predator–prey system with delay

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