Integrability of a class of \(N\)-dimensional Lotka-Volterra and Kolmogorov systems

DOI10.1016/j.jde.2020.02.001zbMath1443.34005OpenAlexW3005116729MaRDI QIDQ2180556

Valentín Ramírez, Jaume Llibre, Rafael O. Ramírez

Publication date: 14 May 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.02.001

zbMATH Keywords

Lotka-Volterra systemscenter problemJacobi multiplierMay-Leonard modelcompletely integrable ordinary differential equationsKolmogorov ordinary differential equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Invariant circles and phase portraits of cubic vector fields on the sphere ⋮ Generalized analytic integrability of a class of polynomial differential systems in \(\mathbb{C}^2\)

Cites Work

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• Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier
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• Integrability and global dynamics of the May-Leonard model
• Complete integrability of vector fields in \(\mathbb{R}^N\)
• Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity
• Qualitative theory of planar differential systems
• On the Asymmetric May--Leonard Model of Three Competing Species
• Generalized Hamiltonian Dynamics

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