An indirect method of finding integrals for three-dimensional quadratic homogeneous systems

DOI10.1016/S0375-9601(98)00317-XzbMath0946.34002MaRDI QIDQ1966744

Zhaonan Liu, Puyun Gao

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

integralsthree-dimensional quadratic homogeneous equations

Mathematics Subject Classification ID

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

Related Items (8)

Local integrability of a family of three-dimensional quadratic systems ⋮ Direct integration method and first integrals for three-dimensional Lotka-Volterra systems ⋮ Integrability and linearizability problems of three dimensional Lotka-Volterra equations of rank-2 ⋮ Hamiltonian structure and first integrals for the Lotka-Volterra systems ⋮ Algebraic decoupling of variables for systems of ODEs of quasipolynomial form ⋮ On the first integrals of Lotka-Volterra systems ⋮ Integrability and linearizability of a family of three-dimensional quadratic systems ⋮ Local integrability and linearizability of three-dimensional Lotka-Volterra systems

Cites Work

• Unnamed Item
• Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
• Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
• Nonlinear Aspects of Competition Between Three Species
• Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
• Hamiltonian structures for the n-dimensional Lotka–Volterra equations

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