Slow–fast dynamics in small trophic chains with habitat loss

Predator–prey models serve as a fertile ground for modeling the emergence of slow–fast dynamics in natural species. In this work, we demonstrate a set of slow–fast predator–prey ecosystems to investigate the impact of habitat loss on ecosystems, using geometric singular perturbation theory (GSPT) as the mathematical framework. Our methodology outlines how to decompose the multi-trophic-level slow–fast system into its slow and fast subsystems. The impacts of habitat loss and environmental changes on the critical manifold of the slow–fast system are discussed. The model is shown to undergo a canard cycle for a range of parameter values. In the Rosenzweig–MacArthur (R–M) predator–prey system, earlier studies did not consider the density-dependent habitat loss of prey, which could lead to the exhibition of canard cycles. However, the inclusion of density-dependent habitat loss mortality in the system can also lead to canard cycles. Graphic abstract