Bifurcation analysis of a diffusive predator-prey model in spatially heterogeneous environment

We investigate positive steady states of a diffusive predator-prey model in spatially heterogeneous environment. In comparison with the spatially homogeneous environment, the dynamics of the predator-prey model of spatial heterogeneity is more complicated. Our studies show that if dispersal rate of the prey is treated as a bifurcation parameter, for some certain ranges of death rate and dispersal rate of the predator, there exist multiply positive steady state solutions bifurcating from semi-trivial steady state of the model in spatially heterogeneous environment, whereas there exists only one positive steady state solution which bifurcates from semi-trivial steady state of the model in homogeneous environment.