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Keyword

Liénard systems

Description: A class of nonlinear differential equation systems used to model oscillations and analyze limit cycles and bifurcations.
OpenAlex ID: keywords/lienard-systems
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering
1995 · Steven H. Strogatz, Ronald F. Fox · Physics Today · 2,583
A survey of isochronous centers
1999 · Javier Chavarriga, Marco Sabatini · Qualitative Theory of Dynamical Systems · 225
The number and stability of limit cycles for planar piecewise linear systems of node–saddle type
2018 · Jiafu Wang, Xiaoyan Chen, et al. · Journal of Mathematical Analysis and Applications · 142
A Predator–Prey Model with Ivlev's Functional Response
1996 · R.E. Kooij, A. Zegeling · Journal of Mathematical Analysis and Applications · 113
Chimeralike states in a network of oscillators under attractive and repulsive global coupling
2015 · Arindam Mishra, Chittaranjan Hens, et al. · Physical Review E · 98
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Isochronous Centers in Planar Polynomial Systems
1997 · C. J. Christopher, J. Devlin · SIAM Journal on Mathematical Analysis · 98
Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
1999 · Colin Christopher, Stephen Lynch · Nonlinearity · 84
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On the Period Function of Liénard Systems
1999 · M. Sabatini · Journal of Differential Equations · 81
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On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
1990 · C. J. Christopher, N. G. Lloyd · Bulletin of the London Mathematical Society · 74
An Algebraic Approach to the Classification of Centers in Polynomial Liénard Systems
1999 · Colin Christopher · Journal of Mathematical Analysis and Applications · 73
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Small-amplitude limit cycles of certain Liénard systems
1988 · N. G. Lloyd, S. Lynch · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 71
Extreme events in a network of heterogeneous Josephson junctions
2020 · Arnob Ray, Arindam Mishra, et al. · Physical review. E · 68
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Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System
2017 · S. Leo Kingston, K. Thamilmaran · International Journal of Bifurcation and Chaos · 60
Liapunov Constants and Hopf Cyclicity of Lienard Systems
1999 · 韩茂安 · 微分方程年刊：英文版 · 60
On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
2010 · Jihua Wang, Dongmei Xiao · Journal of Differential Equations · 57
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Fast Subsystem Bifurcations in a Slowly Varying Liénard System Exhibiting Bursting
1994 · M. Pernarowski · SIAM Journal on Applied Mathematics · 50
Small-Amplitude Limit Cycles in Liénard Systems via Multiplicity
1999 · Armengol Gasull, Joan Torregrosa · Journal of Differential Equations · 48
Small-amplitude limit cycles in polynomial Li�nard systems
1996 · Colin J. Christopher, Noel G. Lloyd · Nonlinear Differential Equations and Applications NoDEA · 48
On the number of limit cycles of polynomial Liénard systems
2012 · Maoan Han, Valery G. Romanovski · Nonlinear Analysis Real World Applications · 44
New lower bounds for the Hilbert number of polynomial systems of Liénard type
2014 · Yanqin Xiong, Maoan Han · Journal of Differential Equations · 41
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Transformation to Lienard form
2000 · Wafaa A. Albarakati, N. G. Lloyd, et al. · DOAJ (DOAJ: Directory of Open Access Journals) · 40
Vibration control for parametrically excited Liénard systems
2005 · Attilio Maccari · International Journal of Non-Linear Mechanics · 39
On the classification of Liénard systems with amplitude-independent periods
2004 · Colin Christopher, James Devlin · Journal of Differential Equations · 38
Isochronicity and commutation of polynomial vector fields
1999 · E. P. Volokitin, V. V. Ivanov · Siberian Mathematical Journal · 37
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Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis
2023 · Ting Chen, Feng Li, et al. · Journal of Differential Equations · 36
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Works count: 793
Citation count: 7,619
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