Darboux method and search of invariants for the Lotka–Volterra and complex quadratic systems

DOI10.1063/1.532852zbMath0986.34032OpenAlexW2071225125MaRDI QIDQ4701839

Laurent Cairó, Marc R. Feix, Jaume Llibre

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532852

zbMATH Keywords

invariantfirst integralLotka-Volterra systempolynomial differential systemDarboux methodcomplex quadratic system

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14)

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Cites Work

• Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires
• Connection between the existence of first integrals and the painlevé property in two-dimensional lotka-volterra and quadratic systems
• On a differential equation of boundary-layer theory
• Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
• Hamiltonian method and invariant search for 2D quadratic systems
• Time-independent invariants of motion for the quadratic system
• Periodic Small-Amplitude Solutions to Volterra's Problem of Two Conflicting Populations and Their Application to the Plasma Continuity Equations