An effective method of counting the number of limit cycles

DOI10.1017/S0027763000018535zbMath0422.34036MaRDI QIDQ3855500

Kazuo Yamato

Publication date: 1979

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

limit cyclesvector fieldsstructure stability

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30)

Related Items

Counting configurations of limit cycles and centers, Bifurcation values for a family of planar vector fields of degree five, Reduction to transversality of curves in the construction of a Dulac function, Dulac functions of planar vector fields, Spline approximations in the problem of estimating the number of limit cycles of autonomous systems on the plane, Effectiveness of the Bendixson-Dulac theorem, Fixed and moving limit cycles for Liénard equations, Bifurcation diagram and stability for a one-parameter family of planar vector fields, A new criterion for controlling the number of limit cycles of some generalized Liénard equations, Some Applications of the Extended Bendixson-Dulac Theorem, Unnamed Item

Cites Work

• Structural stability on two-dimensional manifolds
• On the limit cycles of \(\ddot x+\mu\sin\dot x+x = 0\)
• For all real \(\mu\), \(\ddot x +\mu \sin\dot x+x = 0\) has an infinite number of limit cycles
• On the limit cycles of \(y+\mu F(y')+y = 0\)
• On periodic solutions of the system \(\dot x = y - F(x),\dot y = - g(x)\)
• On the generalized Lienard equation with negative damping
• Qualitative Theory of Codimension-One Foliations