A simple class of quadratic systems

DOI10.1016/0022-0396(86)90075-6zbMath0603.34023OpenAlexW1979949102MaRDI QIDQ1082513

William Andrew Coppel

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0022-0396(86)90075-6

zbMATH Keywords

limit cyclecritical pointquadratic systemplane quadratic system

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

Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Word problems related to derivatives of the displacement map ⋮ Periodic solutions of polynomial non-autonomous differential equations ⋮ Limit cycles of vector fields of the form \(X(v)=Av+f(v)Bv\) ⋮ Limit cycles of polynomial systems with homogeneous non-linearities ⋮ Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems

Cites Work

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• Number of limit cycles of the bounded quadratic system with two finite singular points
• Limit cycles of a class of polynomial vector fields in the plane
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Some problems in the qualitative theory of ordinary differential equations
• Existence, uniqueness, and nonexistence of limit cycles for a class of quadratic systems in the plane
• Limit cycles of planar quadratic differential equations
• A survey of quadratic systems
• Bounded quadratic systems in the plane
• On General Properties of Quadratic Systems