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A discrete-time model with non-monotonic functional response and strong Allee effect in prey. (English) Zbl 1435.92049
Summary: In this paper, we investigate the impact of strong Allee effect on the stability of a discrete-time predator-prey model with a non-monotonic functional response. The dynamics of discrete-time predator-prey models with strong Allee effect is studied earlier. But, the mathematical investigations of predator-prey dynamics in discrete-time set up with Holling type-IV functional response and strong Allee effect in prey are lacking. The proposed model supports the coexistence of two steady states, and the mathematical features of the model are analyzed based on local stability and bifurcation theory. By considering the Allee parameter as the bifurcation parameter, we provide sufficient conditions for the flip and the Neimark-Sacker bifurcations. We observe that Allee parameter plays a significant role in the dynamics of the system.
MSC:
92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
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