A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework
arXiv:2504.10355 · doi:10.1016/j.nonrwa.2025.104534
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.
21 pages, 6 figures
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