Coexistence of one predator and two prey through rapid evolution in predator's feeding choice

In this article, we study the coexistence of one predator and two prey with evolutionary effects. To that end, we formulate a three-time-scale model with rapid adaptive in predator's feeding choice, slow prey growth and superslow predator growth. By using the geometric singular perturbation theory and computing the entry-exit function for multidimensional fast-slow systems, we find that the predator and the two prey coexist in a form of relaxation oscillations between being near the extreme values of feeding choice strategy due to the associated delay of stability loss. It is also found that the predator can coexist with the two prey in the form of an interior equilibrium with a locally optimal feeding choice. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this article, we investigate the coexistence of a predator and two prey species under the influence of evolution. We propose a three-time-scale model that incorporates rapid adaptive behavior in the predator's feeding choice, slow growth in the prey species, and extremely slow growth in the predator. By utilizing geometric singular perturbation theory and computing the entry-exit function for multidimensional fast-slow systems, we discover that the predator and the two prey species can coexist through relaxation oscillations in their feeding choice strategies, which is attributed to the delayed loss of stability. Additionally, we demonstrate that the predator can coexist with the two prey species through an interior equilibrium state with locally optimal feeding choice.