Stability and bifurcation in a delayed predator-prey system with stage structure and functional response

Abstract

In this paper, a delayed predator-prey system with stage structure and Holling type-II functional response is investigated. The local stability of a positive equilibrium and the existence of Hopf bifurcations are established. By using the normal form theory and center manifold reduction, explicit formulae determining the stability, direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate the theoretical results.

Keywords

• Time delay
• stage structure
• stability
• Hopf bifurcation
• functional response