Effects of time delay on a singular predator-prey bioeconomic model

In this paper, a class of singular predator-prey bioeconomic model with time delay is investigated. It is obtained that the interior equilibrium switches from being stable to unstable and then back to stable as the time delay increases. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By numerical simulation, it is indicated that populations variances oscillate with the increase of time delay.