A positively invariant attracting set for a predator-prey model with a non-differentiable functional response (Selecciones Matemáticas, 2022)
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.