Nilpotent singularities and chaos: Tritrophic food chains

Fátima Drubi, Santiago Ibáñez and Paweł Pilarczyk

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: Local bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding this method and describe the main steps to illustrate numerically the chaotic dynamics emerging near these nilpotent singularities. This is a general-purpose method and we hope it can be applied to a huge range of models.

Keywords: Nilpotent singularities; Trophic models; Strange attractors (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307992

DOI: 10.1016/j.chaos.2020.110406

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