Limit cycles of continuous piecewise differential systems formed by linear and quadratic isochronous centers I
Ghermoul, Bilal (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))

Date:	2022
Abstract:	First, we study the planar continuous piecewise differential systems separated by the straight line x = 0 formed by a linear isochronous center in x > 0 and an isochronous quadratic center in x < 0. We prove that these piecewise differential systems cannot have crossing periodic orbits, and consequently they do not have crossing limit cycles. Second, we study the crossing periodic orbits and limit cycles of the planar continuous piecewise differential systems separated by the straight line x = 0 having in x > 0 the general quadratic isochronous center x =-y + x2-y2, x = x(1 + 2y) after an affine transformation, and in x < 0 an arbitrary quadratic isochronous center. For these kind of continuous piecewise differential systems the maximum number of crossing limit cycles is one, and there are examples having one crossing limit cycles. In short for these families of continuous piecewise differential systems we have solved the extension of the 16th Hilbert problem.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Isochronous quadratic centers ; Continuous piecewise linear differential systems ; First integrals
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 1 (January 2022) , art. 2250003, ISSN 1793-6551

DOI: 10.1142/S0218127422500031

Postprint 39 p, 573.8 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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