Spatiotemporal dynamics of a prey-predator model with Allee effect in prey and hunting cooperation in a Holling type III functional response

In this work, we have studied a spatiotemporal prey-predator model with Allee effect in prey and hunting cooperation in predator. In available literature, a prey-dependent functional response is mostly considered to model the prey-predator interaction. But empirical data show that functional response can depend on both prey and predator populations. Here, we have introduced the cooperative hunting in a Holling type III functional response for the predator population and extended the model spatially. Both Turing and non-Turing patterns produced by the diffusion added prey-predator model have been studied in detail. Emphasis is given to the analytical study of the spiral and target patterns applying the amplitude equation through weakly nonlinear analysis. The analytical results are verified with extensive numerical simulations.