Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point

DOI10.2478/tmmp-2021-0018zbMath1498.34087OpenAlexW4205469396MaRDI QIDQ2068682

Aziza Berbache, Ahmed Bendjeddou, Sabah Benadouane

Publication date: 20 January 2022

Published in: Tatra Mountains Mathematical Publications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/tmmp-2021-0018

zbMATH Keywords

first integralplanar polynomial differential systemalgebraic and non-algebraic limit cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (1)

Integrability and non-existence of periodic orbits for a class of Kolmogorov systems

Cites Work

• Explicit non-algebraic limit cycles for polynomial systems
• The limit cycle of the van der Pol equation is not algebraic
• Darboux integrability and the inverse integrating factor.
• Simple Darboux points of polynomial planar vector fields.
• Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations
• NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS
• Liouvillian First Integrals of Differential Equations
• Phase portraits of cubic polynomial vector fields of Lotka–Volterra type having a rational first integral of degree 2
• About a conjecture on quadratic vector fields
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