The global centre for the Liénard system

DOI10.1016/0362-546X(91)90075-CzbMath0734.34033OpenAlexW2006361466MaRDI QIDQ3361164

Jitsuro Sugie

Publication date: 1991

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(91)90075-c

zbMATH Keywords

Liénard systemorbitsclosed curvesglobal centerdeformed mirror symmetryoscillate

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (9)

On the Liénard system which has no periodic solutions ⋮ On the Center of the Generalized Liénard System ⋮ When do all trajectories in the Liénard plane cross the vertical isocline? ⋮ Some criteria of the existence of limit cycles for a planar system of liénard type ⋮ An oscillation criterion for generalized Liénard equations. ⋮ The qualitative behavior of a second-order system with zero diagonal coefficient. ⋮ Intersection with the vertical isocline in the generalized Liénard equations ⋮ Classifying involutions on \(PR(2k)\) up to equivariant cobordism ⋮ On global asymptotic stability of systems of Liénard type

Cites Work

• A necessary and sufficient condition for oscillation of the generalized Liénard equation
• On the qualitative behaviour of solutions of Liénard equation
• On periodic solutions of the system \(\dot x = y - F(x),\dot y = - g(x)\)
• On the generalized Lienard equation with negative damping
• A general equation for relaxation oscillations
• Sur un théorème de A. Filippoff
• On the existence of N periodic solutions of Liénard's equation
• Liénard systems with several limit cycles
• A Differential Equation
• On a Van Der Pol Equation with Odd Coefficients
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