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arXiv · 2504.10355

A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework

Jacopo Borsotti·Mattia Sensi
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Abstract

We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models.

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Jacopo Borsotti, Mattia Sensi. 2025-04-14. A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework. https://doi.org/10.1016/j.nonrwa.2025.104534

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