Cubic Lienard equation with quadratic damping. I

DOI10.1007/BF02670963zbMath0956.34020OpenAlexW74946010MaRDI QIDQ1568230

Yuquan Wang, Zhu-jun Jing

Publication date: 26 February 2001

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02670963

zbMATH Keywords

stabilitylimit cyclesHopf bifurcationexistence and uniquenessqualitative analysiscubic Lienard equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers. ⋮ Cubic Liénard equations with quadratic damping. II.

Cites Work

• On the qualitative behaviour of solutions of Liénard equation
• A necessary and sufficient condition for the existence of a unique nontrivial periodic solution to a class of equations of Lienards type
• Uniqueness of limit cycles for a class of Lienard systems with applications
• Limit-cycles and rotated vector fields
• Uniqueness of limit cycles in liénard-type equations
• On the uniqueness of the periodic solutions of certain Liénard equations
• On existence of periodic orbits for the FitzHugh nerve system
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