Periodic orbits of continuous-discontinuous piecewise differential systems with four pieces separated by the curve xy = 0 and formed by linear Hamiltonian systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics)

Date:	2024
Abstract:	In recent years there has been a significant interest in studying the piecewise differential systems, mainly due to their wide range of applications in modeling natural phenomena. To understand the dynamics of such systems in the plane is a significant challenge, particularly when we want to study their periodic orbits and, more specifically, their limit cycles. Consequently numerous studies have been dedicated to investigate the existence or non-existence of periodic orbits within continuous and discontinuous piecewise differential systems. However to the best of our knowledge, this paper is one of the pioneering works analysing the periodic orbits within a specific class of piecewise differential systems, the ones exhibiting continuity in one part of the separation line while being discontinuous in the other part. Our study analyzes the periodic orbits of the piecewise differential systems formed by four pieces, having the curve xy = 0 as the separation line, and in each piece there is an arbitrary linear Hamiltonian system. Moreover we assume that these piecewise differential systems exhibit continuity along the x-axis while being discontinuous along the y-axis.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Linear focus ; Linear center ; Quadratic weak focus ; Quadratic center ; Limit cycle ; Discontinuous piecewise differential system
Published in:	Dynamics of continuous, discrete and impulsive systems, Vol. 31, Issue 4 (2024) , p. 279-286, ISSN 1918-2538

Adreça alternativa: https://online.watsci.org/abstract_pdf/2024v31/v31n4a-pdf/4.pdf

Postprint 6 p, 252.5 KB

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