Regular and Chaotic Dynamics

, Volume 13, Issue 6, pp 543–556

Integrable Lotka-Volterra systems

Jürgen Moser - 80

DOI: 10.1134/S1560354708060051

Cite this article as:
Bogoyavlenskij, O.I. Regul. Chaot. Dyn. (2008) 13: 543. doi:10.1134/S1560354708060051


Infinite- and finite-dimensional lattices of Lotka-Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka- Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.

Key words

Lax representationHamiltonian structuresCasimir functionsRiemannian surfacesLotka-Volterra systemsintegrable lattices

MSC2000 numbers


Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada
  2. 2.V.A. Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia