Nilpotent singularities and chaos: Tritrophic food chains

Fátima Drubi; Santiago Ibáñez; Paweł Pilarczyk

doi:10.1016/j.chaos.2020.110406

Nilpotent singularities and chaos: Tritrophic food chains

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.

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Category:: Articles
Type:: artykuły w czasopismach
Published in:: CHAOS SOLITONS & FRACTALS no. 142,
ISSN: 0960-0779
Language:: English
Publication year:: 2021
Bibliographic description:: Drubi F., Ibáñez S., Pilarczyk P.: Nilpotent singularities and chaos: Tritrophic food chains// CHAOS SOLITONS & FRACTALS -Vol. 142, (2021), s.110406-
DOI:: Digital Object Identifier (open in new tab) 10.1016/j.chaos.2020.110406
Verified by:: Gdańsk University of Technology