On a diffusive predator-prey model with nonlocal fear effect

A diffusive predator-prey model incorporating the nonlocal fear effect is considered. The stability of the constant equilibria is investigated by using the characteristic equation and Lyapunov functionals. Analyses of steady-state bifurcation are carried out in detail using the Lyapunov-Schmidt procedure. On one hand, compared with the model in the absence of the nonlocal effect, we find that the nonlocal term maintains global stability under some conditions. On the other, some numerical simulations indicate that there may be two coexisting stable nonconstant steady states after introducing a kernel function. (c) 2022 Elsevier Ltd. All rights reserved.