Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integra...

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Veröffentlicht in:Mediterranean journal of mathematics 2021-08, Vol.18 (4), Article 167
Hauptverfasser: Aziz, Waleed, Christopher, Colin, Llibre, Jaume, Pantazi, Chara
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Parameters
Resonance
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Zusammenfassung:We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01809-2