A Diffusive Predator-Prey Model with Spatially Heterogeneous Carrying Capacity

We study local dynamics of a diffusive predator-prey model in a spatially heterogeneous environment,where intrinsic growth rate of the prey is spatially ho-mogeneous,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.