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

Abstract

We present a method to construct superintegrable $n$-component Lotka-Volterra systems with $3n-2$ parameters. We apply the method to Lotka-Volterra systems with $n$ components for $1<n<6$, and present several $n$-dimensional superintegrable families. The Lotka-Volterra systems are in one-to-one correspondence with trees on $n$ vertices.

arXiv comment14 pages, 4 figures

References in corpus (7)

• Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems
• Integrable deformations of Lotka-Volterra systems
• Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization
• Darboux polynomials for Lotka-Volterra systems in three dimensions
• Integrable and superintegrable systems associated with multi-sums of products
• Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
• Trees and superintegrable Lotka-Volterra families

Cited by in corpus (1)

• Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation