Dynamics of a Generalized Rayleigh System
Baldissera, Maíra Duran (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)

Date:	2024
Abstract:	Consider the first order differential system given by (x˙ = y, y˙ = −x + a(1 − y2n)y) where a is a real parameter and the dots denote derivatives with respect to the time t. Such system is known as the generalized Rayleigh system and it appears, for instance, in the modeling of diabetic chemical processes through a constant area duct, where the effect of adding or rejecting heat is considered. In this paper we characterize the global dynamics of this generalized Rayleigh system. In particular we prove the existence of a unique limit cycle when the parameter a≠0.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Rayleigh system ; Limit cycles ; Averaging theory ; Poincaré compactification
Published in:	Differential Equations and Dynamical Systems, Vol. 32, Issue 3 (July 2024) , p. 933-941, ISSN 0974-6870

DOI: 10.1007/s12591-022-00604-z

Available from: 2025-07-31 Postprint

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles