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Liénard equation

Description: The Liénard equation is a nonlinear second-order differential equation used to model oscillatory systems in applied mathematics and physics.
Wikidata ID: wiki/Q2500406
OpenAlex ID: keywords/lienard-equation
On Liénard's equation
1977 · A. Lins, W. de Melo, et al. · Lecture notes in mathematics · 175
Techniques in the Theory of Local Bifurcations: Blow-Up, Normal Forms, Nilpotent Bifurcations, Singular Perturbations
1993 · Freddy Dumortier · Springer eBooks · 158
Differential equations for the heartbeat and nerve impulse
2017 · E. C. Zeeman · Routledge eBooks · 155
Cubic Lienard equations with linear damping
1990 · F Dumortier, C Rousseau · Nonlinearity · 123
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Perturbation from an elliptic Hamiltonian of degree four—IV figure eight-loop
2003 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 121
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Perturbations from an Elliptic Hamiltonian of Degree Four
2001 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 118
The number of small-amplitude limit cycles of Liénard equations
1984 · T. R. Blows, N. G. Lloyd · Mathematical Proceedings of the Cambridge Philosophical Society · 114
Perturbations from an Elliptic Hamiltonian of Degree Four
2001 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 106
On the generalized Liénard equation with negative damping
1972 · John R. Graef · Journal of Differential Equations · 106
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Periodic Solutions of Liénard Equations with Singular Forces of Repulsive Type
1996 · Meirong Zhang · Journal of Mathematical Analysis and Applications · 103
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Periodic solutions of some Liénard equations with singularities
1990 · Patrick Habets, Luis Sanchez · Proceedings of the American Mathematical Society · 103
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More limit cycles than expected in Liénard equations
2007 · Freddy Dumortier, Daniel Panazzolo, et al. · Proceedings of the American Mathematical Society · 102
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Limit cycles of the generalized polynomial Liénard differential equations
2009 · JAUME LLIBRE, ANA CRISTINA MEREU, et al. · Mathematical Proceedings of the Cambridge Philosophical Society · 95
The Kaldor‐Kalecki business cycle model
1999 · A. Krawiec, M. Szydlowski · Annals of Operations Research · 93
Uniqueness of limit cycles for Liénard differential equations of degree four
2011 · Chengzhi Li, Jaume Llibre · Journal of Differential Equations · 84
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Perturbation from an elliptic Hamiltonian of degree four—III global centre
2003 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 83
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Qualitative analysis of a ratio-dependent Holling–Tanner model
2007 · Zhiqing Liang, Hongwei Pan · Journal of Mathematical Analysis and Applications · 76
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On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
1996 · Freddy Dumortier, Chengzhi Li · Nonlinearity · 75
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On the qualitative behaviour of solutions of Liénard equation
1987 · Gabriele Villari · Journal of Differential Equations · 75
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Quadratic Liénard Equations with Quadratic Damping
1997 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 72
The McKean's Caricature of the Fitzhugh--Nagumo Model I. The Space-Clamped System
2003 · Arnaud Tonnelier · SIAM Journal on Applied Mathematics · 69
On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
2008 · Jaume Llibre, Enrique Ponce, et al. · Nonlinearity · 67
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New $\phi^{6}$ ϕ 6 -model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity
2018 · Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, et al. · The European Physical Journal Plus · 65
On explicit exact solutions for the Lienard equation and its applications
2002 · Zhaosheng Feng · Physics Letters A · 64
On the Jacobi Last Multiplier, integrating factors and the Lagrangian formulation of differential equations of the Painlevé–Gambier classification
2009 · A. Ghose Choudhury, Partha Guha, et al. · Journal of Mathematical Analysis and Applications · 61
Works count: 877
Citation count: 6,787
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