Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T00:48:05.753Z Has data issue: false hasContentIssue false
  • English
  • Français

Limit Cycles of Liénard Equations With Non Linear Damping

Published online by Cambridge University Press:  20 November 2018

A.M. Urbina ,
G. León De La Barra ,
M. León De La Barra  and
M. Cañas
A.M. Urbina
Affiliation:
Departamento de Matemâtica Universidad Técnica Federico Santa Maria Casilla 110 - V. Valparaiso Chile
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the Liénard's equation with f(x) polynomial. By using the generalized polar coordinates we establish the maximum possible number of small amplitude limit cycles of such equation in terms of the degree of f(x).

Keywords

34C0534C25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 251 - 256
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Blows, T. R. and Lloyd, N. G., The number of small-amplitude limit cycles of Liénard equations, Math. Proc. Camb. Phil. Soc. 95(1984), 359–366.Google Scholar
2. Dumortier, F. and Rousseau, C., Cubic Liénard equations with linear damping, pre-print, 1989.Google Scholar
3. Lins, A., de, W. Melo and Pugh, C., On Liénard's equation. Lecture Notes in Mathematics, 597 Springer- Verlag, 1977, 335–357.Google Scholar
4. Lyapunov, A., Stability of motion. Mathematics in Science and Engineering, 30, Academic Press, New York, London, 1966.Google Scholar
5. Moussu, R., Symétrie et Forme Normale des Centres et Foyers Dégénérés.Ergod. Th. and Dynam. Systems. 2(1982), 241–251.Google Scholar
6. Staude, U., Uniqueness of periodic solutions of the Liénard equations. Recent Advances in Differential Equations, Academic Press, 1981.Google Scholar