https://doi.org/10.1140/epjb/s10051-025-00952-z
Regular Article - Computational Methods
Slow–fast dynamics in small trophic chains with habitat loss
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
Received:
3
April
2025
Accepted:
6
May
2025
Published online:
25
May
2025
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.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
