Pattern dynamics in a diffusive predator-prey model with hunting cooperations

By considering the hunting cooperations, we propose a diffusive predator-prey model, in which the function response is an increasing function in both predator and prey densities. We then study the pattern structure: (a) Turing space in d(21) - alpha plane is obtained by linear stability analysis, (b) the technique of multiple-time-scale is used to derive the amplitude equations, and finally (c) pattern selection is discussed based on numerical simulations. The results show that the model can present rich pattern structures, and cross-diffusion has a significant impact on species distribution. (C) 2019 Elsevier Ltd. All rights reserved.