Hopf bifurcation in a Volterra prey–predator model with strong kernel

In this paper, a Volterra prey–predator model with distributed delays and strong kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, if the density coefficient of the prey is used as a bifurcation parameter, it is found that Hopf bifurcation occurs for the strong kernel. The direction and stability of the bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.