Stability analysis for a time-delayed nonlinear predator–prey model

In this paper, we investigate the dynamics of a time-delayed prey–predator system with θ-logistic growth. Our investigation indicates that the models based on delayed differential equations (DDEs) with and without delay-dependent coefficient both undergo Hopf bifurcation at their corresponding positive equilibria. It is shown that stability switching occurs for the interior equilibrium of the model with delay-dependent coefficient. For the DDEs model without delay-dependent coefficient, increased time delay may destabilize a stable interior equilibrium.