Quadratic systems with an invariant conic having Darboux invariants

DOI10.1142/S021919971750033XzbMath1394.34055MaRDI QIDQ4563678

Jaume Llibre, Regilene D. S. Oliveira

Publication date: 4 June 2018

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

quadratic vector fieldphase portraitDarboux invariant

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) Symmetries, invariants of ordinary differential equations (34C14) Invariant manifolds for ordinary differential equations (34C45)

Related Items (4)

Dynamics and Darboux integrability of the \(D_2\) polynomial vector fields of degree 2 in \(\mathbb{R}^3\) ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Unnamed Item ⋮ Darboux integrability and dynamics of the Basener-Ross population model

Cites Work

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• Darboux invariants for planar polynomial differential systems having an invariant conic
• From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields
• Geometry of quadratic differential systems in the neighborhood of infinity
• Qualitative theory of planar differential systems
• Phase portraits of quadratic Lotka–Volterra systems with a Darboux invariant in the Poincaré disc
• Classification of Continuous Flows on 2-Manifolds
• Darbouxian first integrals and invariants for real quadratic systems having an invariant conic
• Quadratic systems with invariant straight lines of total multiplicity two having Darboux invariants

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