Alexander Grin, Klaus R. Schneider

Location of the Limit Cycle for a Class of Liénard Systems by Means of Dulac-Cherkas Functions

Dulac-Cherkas functions can be used to estimate the number of limit cycles and to approximate their location. We consider a class of Liénard systems containing the van der Pol system as a special case and present two approaches to construct Dulac-Cherkas functions. By means of two Dulac-Cherkas functions, we improve the Poincaré-Bendixson annulus for the van der Pol system which has been derived in our previous paper [A. A. Grin and K. R. Schneider, Global algebraic Poincaré-Bendixson annulus for the van der Pol system. (Russian) Differ. Uravn. 58 (2022), no. 3, 291-300; translation in Differ. Equ. 58
(2022), no. 3, 285-295].

Mathematics Subject Classification: 34C05, 34C07

Key words and phrases: Limit cycle, Liénard system, van der Pol system, Dulac-Cherkas function, Poincaré-Bendixson annulus