Pattern dynamics in a diffusive predator-prey model with hunting cooperations. (English) Zbl 1489.92128
Summary: 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.
MSC:
| 92D25 | Population dynamics (general) |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 92D40 | Ecology |
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