Lower bounds for the number of limit cycles in a generalised Rayleigh-Liénard oscillator
Euzébio, R (Federal University of Goiás. Institute of Mathematics and Statistics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tonon, Durval José (Federal University of Goiás. Institute of Mathematics and Statistics)

Date:	2022
Abstract:	In this paper a generalised Rayleigh-Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approach consists in perform suitable changes in the sign of some specific parameters and apply Poincaré-Bendixson theorem for assure the existence of limit cycles. In particular, the algorithm for obtaining the limit cycles through the referred approach is explicitly exhibited. The main techniques applied in this study are the Lyapunov constants and the Melnikov method. The obtained results contemplate the simultaneity of limit cycles of small amplitude and medium amplitude, the former emerging from a weak focus equilibrium and the latter from homoclinic or heteroclinic saddle connections.
Grants:	Ministerio de Ciencia e Innovación MJM2016-77278-8 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Rayleigh Liénard oscillator ; Limit cycles ; Lyapunov constants ; Melnikov function
Published in:	Nonlinearity, Vol. 35, Issue 8 (August 2022) , p. 3883-3906, ISSN 1361-6544

DOI: 10.1088/1361-6544/ac7691

Postprint 22 p, 367.9 KB

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