Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator

Author:

Euzébio Rodrigo DORCID,Llibre JaumeORCID,Tonon Durval JORCID

Abstract

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.

Funder

Agència de Gestió d’Ajuts Universitaris i de Recerca

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação de Amparo à Pesquisa do Estado de Goiás

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Ministerio de Ciencia, Innovación y Universidades

H2020 European Research Council

Publisher

IOP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

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