Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems

DOI10.1063/1.532621zbMath0929.37021arXiv1910.02723OpenAlexW3101587594MaRDI QIDQ4701549

Víctor Fairén, Benito Hernández-Bermejo

Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/1910.02723

zbMATH Keywords

Poisson structureLotka-Volterra systemssymplectic foliationDarboux canonical representation

Mathematics Subject Classification ID

Related Items (24)

Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers ⋮ Biochemical systems theory: a review ⋮ Symplectic realizations and symmetries of a Lotka-Volterra type system ⋮ On a Hamiltonian version of a three-dimensional Lotka-Volterra system ⋮ Linear Darboux polynomials for Lotka–Volterra systems, trees and superintegrable families ⋮ New global solutions of the Jacobi partial differential equations ⋮ Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems ⋮ Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems ⋮ Computing Casimir invariants from Pfaffian systems ⋮ Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems ⋮ Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems ⋮ Lotka-Volterra equations in three dimensions satisfying the Kowalevski-Painlevé property ⋮ Integrable deformations of Lotka-Volterra systems ⋮ Local stability and Lyapunov functionals for \(n\)-dimensional quasipolynomial conservative systems ⋮ Characterization, global analysis and integrability of a family of Poisson structures ⋮ New solutions of the Jacobi equations for three-dimensional Poisson structures ⋮ Characterization and global analysis of a family of Poisson structures ⋮ One solution of the 3D Jacobi identities allows determining an infinity of them ⋮ Separation of variables in the Jacobi identities ⋮ A new class of integrable Lotka-Volterra systems ⋮ Generalized results on the role of new-time transformations in finite-dimensional Poisson systems ⋮ Algebraic decoupling of variables for systems of ODEs of quasipolynomial form ⋮ Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions ⋮ Stability conditions and Lyapunov functions for quasi-polynomial systems

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