Spatial dynamics of nonlinear prey–predator models with prey migration and predator switching

The present paper deals with two prey–predator models, one with prey group defence and the other without it. The prey species is assumed to live in two distinct habitats and the predator species has the tendency of switching between the habitats. The models are analyzed regarding stability and bifurcation aspects for the cases where the switching index has the values n = 1 and 2. To model prey dispersal between the habitats, a spatial extension of both the models are considered using physical diffusion of the concerned species. Criteria for diffusion-driven instability are derived and interpreted ecologically. A comparative study of the spatial models are carried out. Numerical simulations are carried out to support analytical findings.