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 as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time 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 . Finally, numerical simulations are investigated to support our theoretical results. © 2016 Elsevier B.V., All rights reserved.