Spatiotemporal dynamics of a delayed diffusive ratio-dependent predator-prey model with fear effect

By considering that there is a delay on the impact of fear to the growth rate of prey, we consider a delayed diffusive predator-prey model with fear effect. First, we give some conditions of the existence of the equilibria. Then, sufficient conditions for the occurrence of Turing, Hopf and Turing-Hopf bifurcation are also obtained. Furthermore, the global asymptotic stability of the positive equilibrium is studied. Finally, some numerical simulations are presented to verify our theoretical results. It shows that the system has various spatiotemporal patterns induced by delay.

Automated summary

In this study, a delayed diffusive predator-prey model with fear effect is considered due to the delay in the impact of fear on the growth rate of prey. The existence of equilibria, occurrence of Turing, Hopf and Turing-Hopf bifurcation, and global asymptotic stability of the positive equilibrium are analyzed, with various spatiotemporal patterns induced by delay confirmed through numerical simulations.