Existence, uniqueness, and nonexistence of limit cycles for a class of quadratic systems in the plane

DOI10.1016/0022-0396(84)90037-8zbMath0493.34025OpenAlexW2001377067MaRDI QIDQ1168479

Lawrence M. Perko, Shihlung Shue

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(84)90037-8

zbMATH Keywords

limit cyclesBendixson-Dulac criterionquadratic systemsglobal behaviorLienard's equationglobal phase portraitscomputer plots

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (4)

A simple class of quadratic systems ⋮ On the Accumulation of Limit Cycles ⋮ Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems ⋮ Global Families of Limit Cycles of Planar Analytic Systems

Cites Work

• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Über das Auftreten von Wirbeln und Strudeln (geschlossener und spiraliger Integralkurven) in der Umgebung rationaler Unbestimmtheitsstellen
• Bounded quadratic systems in the plane
• Limit-cycles and rotated vector fields
• Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem
• On General Properties of Quadratic Systems
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