On the limit cycles of quadratic differential systems.

DOI10.1007/s101140100167zbMath1035.34018OpenAlexW2313754844MaRDI QIDQ1565999

Xiang Zhang

Publication date: 2002

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140100167

zbMATH Keywords

limit cycleergodicityquadratic differential system

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

• Quadratic vector fields in the plane have a finite number of limit cycles
• Non-existence of limit cycle around a weak focus of order three for any quadratic system
• Hilbert's 16th problem for quadratic vector fields
• Weak focus, limit cycles, and bifurcations for bounded quadratic systems
• Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem
• Nonexistence of stable currents in submanifolds of a product of two spheres
• Ergodicity of limit cycles in quadratic systems
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