Integrability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities

DOI10.1007/s10440-012-9772-5zbMath1280.34034OpenAlexW2042337985MaRDI QIDQ1947016

Valery G. Romanovski, Brigita Ferčec, Yi-rong Liu, Jaume Giné

Publication date: 11 April 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-012-9772-5

zbMATH Keywords

integrabilitylinearizabilitypolynomial vector fieldpolynomial differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (14)

Integrability of resonant saddles in a complex differential system ⋮ The solution of the \(1:-3\) resonant center problem in the quadratic case ⋮ Analytic integrability of certain resonant saddle ⋮ Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems ⋮ On integrability conditions and limit cycle bifurcations for polynomial systems ⋮ On the formal integrability problem for planar differential systems ⋮ Integrability of complex planar systems with homogeneous nonlinearities ⋮ The center problem for a \({1:-4}\) resonant quadratic system ⋮ Centers and isochronous centers for generalized quintic systems ⋮ Center conditions for nilpotent cubic systems using the Cherkas method ⋮ A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ Integrability of Lotka–Volterra Planar Complex Cubic Systems ⋮ New family of centers of planar polynomial differential systems of arbitrary even degree

Uses Software

• FGb
• SINGULAR
• primdec

Cites Work

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