Dynamic properties of a delayed predator–prey system with Ivlev-type functional response

Abstract

In this paper, the dynamical behavior of a modified predator–prey system with time delay is investigated. By regarding the time delay as the bifurcation parameter, we study the impact of the time delay on the dynamics of the system. The analysis shows that Hopf bifurcation can occur as the time delay passes some critical values. By employing the normal form theory and the center manifold reduction for functional differential equation, some sufficient conditions are derived for the direction and stability of the Hopf bifurcation. Finally, to verify our theoretical predictions, some numerical simulations are also included.