Linear Darboux polynomials for Lotka–Volterra systems, trees and superintegrable families

DOI10.1088/1751-8121/ACE0E9arXiv2303.00229MaRDI QIDQ6116382

David I. McLaren, Peter H. van der Kamp, Gilles Reinout Willem Quispel, Benjamin K. Tapley

Publication date: 18 July 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.00229

zbMATH Keywords

Lotka-Volterra systemstreesDarboux polynomialssuperintegrability

Mathematics Subject Classification ID

Numerical analysis (65-XX) Ordinary differential equations (34-XX)

Cites Work

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• Integrable Lotka-Volterra systems
• Integrable deformations of Lotka-Volterra systems
• Dynamics of the attractor in the Lotka-Volterra equations
• Integrable and non-integrable Lotka-Volterra systems
• Lotka-Volterra systems satisfying a strong Painlevé property
• Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
• Elementary First Integrals of Differential Equations
• Connection between the existence of first integrals and the painlevé property in two-dimensional lotka-volterra and quadratic systems
• Liouville integrability and superintegrability of a generalized Lotka–Volterra system and its Kahan discretization
• Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions
• Darboux First Integral Conditions and Integrability of the 3D Lotka-Volterra System
• Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems
• Hamiltonian structures for the n-dimensional Lotka–Volterra equations
• Morphisms and automorphisms of skew-symmetric Lotka–Volterra systems*
• Integrable and superintegrable systems associated with multi-sums of products

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