Sébastien Neukirch Institut Jean le Rond d'Alembert Centre National de la Recherche Scientifique Université Pierre et Marie Curie Paris, France tel: +33 1 44 27 72 61 fax : +33 1 44 27 52 59 e-mail: sebastien.neukirch (-atat-) upmc.fr

Improving a method for the study of limit cycles of the Liénard equation

Hector Giacomini & Sébastien Neukirch

Physical Review E  57 #6 (1998) 6573

Abstract : In recent papers we have introduced a method for the study of limit cycles of the Li\'enard system~: $\dot{x}=y-F(x) , \dot{y}=-x$ , where $F(x)$ is an odd polynomial. The method gives a sequence of polynomials $R_n(x)$, whose roots are related to the number and location of the limit cycles, and a sequence of algebraic approximations to the bifurcation set of the system. In this paper, we present a variant of the method that gives very important qualitative and quantitative improvements.

PACS numbers : 05.45.+b , 02.30.Hq , 02.60.Lj , 03.20.+i

Key words : Liénard equation, limit cycles