Abstract: We considered a predator-prey model with fear effect and spatial heterogeneity. Firstly, we gave the local asymptotic stability of trivial and semi-trivial solutions by using Riesz-Schauder theory. Secondly, we gave the global attractivity of trivial and semi-trivial solutions by using the principle of comparison. Finally, we gave the existence of a positive steady-state solution by using the fixed point theorem. The results show that fear effect and spatial heterogeneity have significant effects on the properties of steady-state solutions of the model.

Key words: predator-prey model, Holling Ⅲ function, fear effect, spatial heterogeneity