Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions

DOI10.1142/S1402925109000261zbMath1192.34005arXiv0810.3103OpenAlexW2152096992MaRDI QIDQ3655548

Y. T. Christodoulides, Pantelis A. Damianou

Publication date: 8 January 2010

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

Full work available at URL: https://arxiv.org/abs/0810.3103

zbMATH Keywords

integrabilityDarboux polynomialsLotka-Volterra system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (12)

Linear Darboux polynomials for Lotka–Volterra systems, trees and superintegrable families ⋮ Integrability and linearizability of symmetric three-dimensional quadratic systems ⋮ Integrability of 3-dim polynomial systems with three invariant planes ⋮ Local integrability of a family of three-dimensional quadratic systems ⋮ Integrability and linearizability of three dimensional vector fields ⋮ Integrable and non-integrable Lotka-Volterra systems ⋮ Integrable deformations of Lotka-Volterra systems ⋮ Integrability and linearizability problems of three dimensional Lotka-Volterra equations of rank-2 ⋮ Invariant algebraic surfaces of the FitzHugh-Nagumo system ⋮ Three-dimensional Lotka-Volterra systems with 3:\(-1\):2-resonance ⋮ Integrability and linearizability of a family of three-dimensional quadratic systems ⋮ Local integrability and linearizability of three-dimensional Lotka-Volterra systems

Cites Work

• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• On the complete and partial integrability of non-Hamiltonian systems
• Three integrable Hamiltonian systems connected with isospectral deformations
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• Rational integration of the Lotka-Volterra system
• Darboux polynomials and first integrals of natural polynomial Hamiltonian systems
• Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
• Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
• Darboux integrability for 3D Lotka-Volterra systems
• On the Toda Lattice. II: Inverse-Scattering Solution
• Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems
• On the polynomial first integrals of the (a,b,c) Lotka–Volterra system
• Lie symmetries and invariants of the Lotka–Volterra system

This page was built for publication: Darboux Polynomials for Lotka–Volterra Systems in Three Dimensions