scientific article; zbMATH DE number 7329816

zbMath1457.34051MaRDI QIDQ5857202

Rachid Boukoucha, Mouna Yahiaoui

Publication date: 30 March 2021

Full work available at URL: http://www.math.md/publications/basm/issues/y2019-n3/13140/

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zbMATH Keywords

limit cycleinvariant algebraic curveRiccati equationfirst integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27)

Cites Work

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• Explicit non-algebraic limit cycles for polynomial systems
• The limit cycle of the van der Pol equation is not algebraic
• On the exact limit cycle for some class of planar differential systems
• Qualitative theory of planar differential systems
• Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations
• On the dynamics of a class of rational Kolmogorov systems
• Algebraic limit cycles in polynomial systems of differential equations

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