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Bifurcation Analysis of a Predator–Prey Model with Allee Effect and Fear Effect in Prey and Hunting Cooperation in Predator by Anuj Kumar Umrao; Prashant K. Srivastava is a Mathematics article available to read on EtoBox.

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Studying predator-prey interactions with the help of mathematical modeling is helpful in understanding the mechanism, making informed decisions about their management and conservation, and estimating the behavior and dynamics of ecological systems. In this paper, we have explored the dynamics of a predator-prey model with the fear effect and Allee effect in prey and hunting cooperation in predator species. First, we prove the wellposedness of the system, which is followed by results related to the existence and stability of biologically feasible equilibrium points for the weak Allee effect as well as for the strong Allee effect. We have shown that the model exhibits a variety of bifurcations, including saddle-node, transcritical, and Hopf-bifurcation. Numerical simulation reveals that the conversion rate of predator plays an important role in the stability switching. It is observed that fear has both stabilizing and destabilizing effects depending on hunting cooperation and conversion efficiency of predators. The system experiences persistence or bistability for the weak Allee effect, whereas bistability and tristability are observed in the presence of strong Allee effect. We found

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Author

Anuj Kumar Umrao; Prashant K. Srivastava

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)