For all real \(\mu\), \(\ddot x +\mu \sin\dot x+x = 0\) has an infinite number of limit cycles

DOI10.1016/0022-0396(69)90093-XzbMath0175.09602MaRDI QIDQ2532847

Robert N. D'heedene

Publication date: 1969

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

zbMATH Keywords

ordinary differential equationsinfinite number of limit cycles

Mathematics Subject Classification ID

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

Related Items (8)

Global dynamics of the Josephson equation in \(TS^1\) ⋮ Existence of limit cycles for generalized Liénard equations ⋮ An effective method of counting the number of limit cycles ⋮ Unnamed Item ⋮ On the limit cycles of \(y+\mu F(y')+y = 0\) ⋮ On periodic solutions of the system \(\dot x = y - F(x),\dot y = - g(x)\) ⋮ Existence and stability of periodic solutions of \(\ddot y-\mu F(\dot y) +y=0\). ⋮ LIE SERIES TECHNIQUE, LIMIT CYCLE SYSTEMS AND DYNAMICAL INTEGRATION

Cites Work

• On the limit cycles of \(\ddot x+\mu\sin\dot x+x = 0\)
• A general equation for relaxation oscillations
• Unnamed Item
• Unnamed Item

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