A positively invariant attracting set for a predator-prey model with a non-differentiable functional response
DOI:
https://doi.org/10.17268/sel.mat.2022.02.02Keywords:
predator-prey model, invariant set, functional response.Abstract
In this work, the ecologically well-posedness of a predator-prey model is demonstrated by showing that a region of the first quadrant is a positively invariant attracting set for the solutions of that model. The predator-prey model considers logistic-type growth in both populations and a non-differentiable functional response that generalizes previous ones. Due to non-differentiability, there is no uniqueness of solutions, and the standard methodology cannot be applied directly. Topological equivalences, geometrical arguments, and the Poincare-Bendixson theorem are used to obtain our result.
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