Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-prey Model with Fear Effect

In this paper, we investigate a diffusive predator-prey model with fear effect. It is shown that, for the linear predator functional response case,the positive constant steady state is globally asymptotically stable if it ex-ists. On the other hand, for the Holling type II predator functional response case, it is proved that there exist no nonconstant positive steady states for large conversion rate. Our results limit the parameters range where complex spatiotemporal pattern formation can occur.