Chaos control in a discrete-time predator-prey model with weak Allee effect. (English) Zbl 1401.37096
Summary: The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times. In this paper, we investigate the impact of weak Allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional response. The mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter. We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases. Further, we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium. Our analytical findings are illustrated through numerical simulations.
MSC:
| 37N25 | Dynamical systems in biology |
| 39A28 | Bifurcation theory for difference equations |
| 39A30 | Stability theory for difference equations |
| 39A33 | Chaotic behavior of solutions of difference equations |
| 39A60 | Applications of difference equations |
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