On quadratic systems with a degenerate critical point

DOI10.1216/rmjm/1181072107zbMath0855.34032OpenAlexW2010861280MaRDI QIDQ1915749

Armengol Gasull, Rafel Prohens

Publication date: 3 February 1997

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL26-1/contents/contents.htm

zbMATH Keywords

normal formsbifurcation diagramsplane partraitsquadratic vector fields on the real plane

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Cites Work

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• Quadratic vector fields in the plane have a finite number of limit cycles
• Phase portraits for quadratic systems with a higher order singularity with two zero eigenvalues
• Quadratic systems with a unique finite rest point
• Rotated vector fields and the global behavior of limit cycles for a class of quadratic systems in the plane
• Some theorems on the existence, uniqueness, and nonexistence of limit cycles for quadratic systems
• A survey of quadratic systems
• Sur les points singuliers multiples de systèmes dynamiques dans \(R^ 2\)
• Limit-cycles and rotated vector fields

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