Turing-Hopf bifurcation of a delayed diffusive predator-prey system with chemotaxis and fear effect

In this paper, we consider the impacts of the chemotaxis and delay on the dynamics of a diffusive predator-prey system with fear effect under the Neumann boundary conditions. Regarding chemotaxis coefficient and delay as bifurcation parameters, the existence of the codimension-two Turing-Hopf bifurcation is studied by analyzing the associated characteristic equation. We deduce that chemotaxisdriven Turing bifurcation and discrete delay-driven Hopf bifurcation can occur simultaneously. Finally, spatially homogeneous periodic oscillation, spatial patterns and spatiotemporal patterns appear near Turing-Hopf bifurcation by numerical simulations. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the dynamics of a diffusive predator-prey system with fear effect under Neumann boundary conditions, considering the impacts of chemotaxis and delay. It is found that chemotaxis-driven Turing bifurcation and discrete delay-driven Hopf bifurcation can occur simultaneously, leading to spatially homogeneous periodic oscillation, spatial patterns, and spatiotemporal patterns near the Turing-Hopf bifurcation through numerical simulations.