(untitled) (Journal of Partial Differential Equations, 2023)
We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment, where intrinsic growth rate of the prey is spatially homogeneous, whereas carrying capacity of the habitat is spatially inhomogeneous. In comparison with the existing predator-prey models, the stability of semi-trivial steady state of this model displays distinct properties. For example, for certain intermediate ranges of the death rate of the predator, the semi-trivial steady state can change its stability at least once as the dispersal rate of the prey varies from small to large, while the stability of the semi-trivial steady state is immune from the dispersal rate of the predator.