In this paper we built a stability region around the origin for the Liénard equation (4) to ensure stability and boundedness of solutions of this equation, without making use of the classical Second Method of Lyapunov. We compare our result with some others proposed by different authors.
| Published in | Pure and Applied Mathematics Journal (Volume 3, Issue 4) |
| DOI | 10.11648/j.pamj.20140304.12 |
| Page(s) | 87-91 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Lyapunov, Trajectories, Asymptotic Equilibrium
| [1] | Acosta, J., L. M. Lugo, J. E. Nápoles V. and S. I. Noya (2013)-“On some qualitative properties of a nonautonomous Liénard equation”, submitted. |
| [2] | Guidorizzi, H. L. (1996)-“The family of functions S,k and the Liénard equation”, Tamkang J. of Math. 27, 37-54. |
| [3] | Hasan, Y. Q. and L. M. Zhu (2007)-“The bounded solutions of Liénard equation”, J. Applied Sciences 7(8), 1239-1240. |
| [4] | LaSalle, J. P. (1960)-“Some Extensions of Lyapunov’s Second Method”, IRE Transactions on Circuit Theory, Dec, 520-527. |
| [5] | Lugo L. M., J. E. Nápoles V. and S. I. Noya (2013)-“About a region of boundedness for some nonautonomous Lienard’s Equation”, Annual Meeting of the UMA, Universidad Nacional de Rosario, September 17-20 (Spanish). |
| [6] | Lyapunov, A. M. (1949)-“Problème general de la stabilité du movement”, Annals of Math. Studies, No.17, Princeton University Press, Princeton, N.J. |
| [7] | Lyapunov, A. M. (1966)-“Stability of Motion”, Academic Press, New-York & London, 1966. |
| [8] | Lyapunov, A. M. (1992)-“The General Problem of the Stability of Motion”, (A. T. Fuller trans.) Taylor & Francis, London 1992. |
| [9] | Miller, R. K. and A. N. Michel (1982)-„Ordinary Differential Equation“, New York, Lawa Stat University. |
| [10] | Nápoles Valdes, J. E. (2000)-“On the boundedness and global asymptotic stability of Liénard equation with restoring term”, Revista de la Unión Matemática Argentina 41(4), 47-59. |
| [11] | Nápoles, J. E. and A. I. Ruiz (1997)-“Convergence in nonlinear systems with a forcing term”, Revista de Matemática: Teoría y Aplicaciones 4(1): 1-4. |
| [12] | Yadeta, Z. (2013)-“Lyapunov´s Second Method for Estimating Region of Asymptotic Stability”, Open Science Repository Mathematics, online, doi: dx.doi.org/10.7392/Mathematics.70081944, available in http://www.open-science-repository.com/lyapunovs-second-method-for-estimating-region-of-asymptotic-stability.html |
| [13] | Yoshizawa, T. (1966)-“Stability theory by Liapunov´s Second Method”, The Math. Soc. of Japan. |
APA Style
Luciano Miguel Lugo, Juan Eduardo Nápoles Valdés, Samuel Iván Noya. (2014). On the Construction of Regions of Stability. Pure and Applied Mathematics Journal, 3(4), 87-91. https://doi.org/10.11648/j.pamj.20140304.12
ACS Style
Luciano Miguel Lugo; Juan Eduardo Nápoles Valdés; Samuel Iván Noya. On the Construction of Regions of Stability. Pure Appl. Math. J. 2014, 3(4), 87-91. doi: 10.11648/j.pamj.20140304.12
AMA Style
Luciano Miguel Lugo, Juan Eduardo Nápoles Valdés, Samuel Iván Noya. On the Construction of Regions of Stability. Pure Appl Math J. 2014;3(4):87-91. doi: 10.11648/j.pamj.20140304.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.20140304.12,
author = {Luciano Miguel Lugo and Juan Eduardo Nápoles Valdés and Samuel Iván Noya},
title = {On the Construction of Regions of Stability},
journal = {Pure and Applied Mathematics Journal},
volume = {3},
number = {4},
pages = {87-91},
doi = {10.11648/j.pamj.20140304.12},
url = {https://doi.org/10.11648/j.pamj.20140304.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140304.12},
abstract = {In this paper we built a stability region around the origin for the Liénard equation (4) to ensure stability and boundedness of solutions of this equation, without making use of the classical Second Method of Lyapunov. We compare our result with some others proposed by different authors.},
year = {2014}
}
TY - JOUR T1 - On the Construction of Regions of Stability AU - Luciano Miguel Lugo AU - Juan Eduardo Nápoles Valdés AU - Samuel Iván Noya Y1 - 2014/08/30 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.20140304.12 DO - 10.11648/j.pamj.20140304.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 87 EP - 91 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20140304.12 AB - In this paper we built a stability region around the origin for the Liénard equation (4) to ensure stability and boundedness of solutions of this equation, without making use of the classical Second Method of Lyapunov. We compare our result with some others proposed by different authors. VL - 3 IS - 4 ER -
Information
Email: