Phase portraits of quadratic Lotka–Volterra systems with a Darboux invariant in the Poincaré disc

DOI10.1142/S0219199713500417zbMath1309.34005OpenAlexW1998894406MaRDI QIDQ2937030

Yudy Bolaños, Jaume Llibre, Claudia Valls

Publication date: 7 January 2015

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

Full work available at URL: https://doi.org/10.1142/s0219199713500417

zbMATH Keywords

phase portraitPoincaré compactificationPoincaré discDarboux invariantquadratic Lotka-Volterra systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14)

Related Items

Quadratic systems with an invariant conic having Darboux invariants, Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems, Quantitative analysis of competition models, Darboux invariants for planar polynomial differential systems having an invariant conic

Cites Work

• Canonical forms of real homogeneous quadratic transformations
• Classification and Analysis of two-dimensional real homogeneous quadratic differential equation systems
• On the differentiability of first integrals of two dimensional flows
• Darboux method and search of invariants for the Lotka–Volterra and complex quadratic systems
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