A Family of Periodic Orbits in the Liénard Differential Systems

Zouhair Diab; Juan L. G. Guirao; Amar Makhlouf; Huatao Chen

doi:10.2478/udt-2025-0002

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A Family of Periodic Orbits in the Liénard Differential Systems

Uniform distribution theory

Volume 20 (2025): Issue 1 (May 2025)

By: Zouhair Diab, Juan L. G. Guirao, Amar Makhlouf and Huatao Chen

Open Access

|Jun 2025

Abstract

In this paper, we investigate the existence of a family of periodic orbits for the Liénard systems by expressing these systems as a Hamiltonian system with two degrees of freedom The main technique applied here is the averaging theory.

References

S. Alhowaity, E. I. Abouelmagd, Z. Diab, and J. L. Guirao, Calculating periodic orbits of the Hénon-Heiles system, Frontiers in Astronomy and Space Sciences 9 (2023), 945236.
Search in Google Scholar Back to article
A. Buica and J. Llibre, Averaging methods for finding periodic orbits via Brouwer degree, Bulletin des Sciences Mathématiques 128 (2004), 7-22.
Search in Google Scholar Back to article
Z. Feng, The first-integral method to the Burgers-Korteweg-de Vries equation, J Phys A (Math Gen) 35 (2002) 343{9.
Search in Google Scholar Back to article
J. Guckenheimer, Dynamics of the van der Pol equation, IEEE Trans Circuits Systems 27 (1980) 983-9.
Search in Google Scholar Back to article
J. M. Ginoux, J. Llibre, A family of periodic orbits for the extended Hamiltonian system of the Van der Pol oscillator, Journal of Geometry and Physics 183 (2023), 104705.
Search in Google Scholar Back to article
J. Llibre, D.D. Novaes and M.A. Teixeira, Higher order averaging theory for finding periodic solutions via Brouwer degree, Nonlinearity 27 (2014), 563-583.
Search in Google Scholar Back to article
J. Llibre, L. Jiménez-Lara, Periodic orbits and non-integrability of Hénon-Heiles systems, Journal of Physics A: Mathematical and Theoretical, 44 (2011), 205103.
Search in Google Scholar Back to article
J. A. Sanders F. Verhulst and J. Murdock, Averaging Methods in Nonlinear Dynamical Systems, Second edition, Applied Mathematical Sciences 59, Springer, New York, 2007.
Search in Google Scholar Back to article
F. Verhulst, Nonlinear Di erential Equations and Dynamical Systems, Universitext, Springer, 1991.
Search in Google Scholar Back to article
ZF. Zhang, T. Ding, W. Huang, ZX. Dong, Qualitative theory of differential equations, Peking: Science Press 1985.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/udt-2025-0002 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 16 - 23

Submitted on: Dec 2, 2025

Accepted on: Feb 14, 2025

Published on: Jun 3, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Related subjects:

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2025 Zouhair Diab, Juan L. G. Guirao, Amar Makhlouf, Huatao Chen, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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