Algebraic limit cycle of degree 2 for linear type center plus cubic homogeneous polynomial differential systems

DOI10.1007/S10883-024-09722-ZMaRDI QIDQ6667655

Yulin Zhao, Yuzhou Tian, Luping Wang

Publication date: 20 January 2025

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

zbMATH Keywords

invariant algebraic curverotated vector fieldsalgebraic limit cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Cites Work

• Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Classification of quadratic systems admitting the existence of an algebraic limit cycle
• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré.
• Invariant algebraic curves of large degree for quadratic system
• Algebraic limit cycles of degree 4 for quadratic systems
• Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps
• Qualitative theory of planar differential systems
• Limit-cycles and rotated vector fields
• On a Result of Darboux
• Algebraic limit cycles in polynomial systems of differential equations
• Uniqueness of algebraic limit cycles for quadratic systems
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