Limit cycles of planar quadratic differential equations

DOI10.1016/0022-0396(84)90157-8zbMath0498.34018OpenAlexW2015105057MaRDI QIDQ1171203

Kumpati S. Narendra, Daniel E. Koditschek

Publication date: 1984

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

Full work available at URL: https://repository.upenn.edu/cgi/viewcontent.cgi?article=1484&context=ese_papers

zbMATH Keywords

control theoryunique equilibriumquadratic differential equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (9)

A simple class of quadratic systems ⋮ Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Limit cycles of vector fields of the form \(X(v)=Av+f(v)Bv\) ⋮ Limit cycles of a class of polynomial vector fields in the plane ⋮ Adaptive control of flexible link manipulators using a pseudolink dynamic model ⋮ Limit cycles of polynomial systems with homogeneous non-linearities ⋮ Limit cycles of a class of polynomial systems ⋮ Controllability of bilinear systems ⋮ Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems

Cites Work

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• Some problems in the qualitative theory of ordinary differential equations
• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Classification and Analysis of two-dimensional real homogeneous quadratic differential equation systems
• A survey of quadratic systems
• Bounded quadratic systems in the plane
• Stabilizability of second-order bilinear systems
• The stability of second-order quadratic differential equations
• Lyapunov functions for quadratic differential equations with applications to adaptive control

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