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Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)

Date: 2019
Abstract: We apply the averaging theory of high order for computing the limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. These discontinuous piecewise differential systems are formed by two either quadratic, or cubic polynomial differential systems separated by a straight line. We compute the maximum number of limit cycles of these discontinuous piecewise polynomial perturbations of the linear center, which can be obtained by using the averaging theory of order n for n = 1, 2, 3, 4, 5. Of course these limit cycles bifurcate from the periodic orbits of the linear center. As it was expected, using the averaging theory of the same order, the results show that the discontinuous quadratic and cubic polynomial perturbations of the linear center have more limit cycles than the ones found for continuous and discontinuous linear perturbations. Moreover we provide sufficient and necessary conditions for the existence of a center or a focus at infinity if the discontinuous piecewise perturbations of the linear center are general quadratic polynomials or cubic quasi–homogenous polynomials.
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció MINECO/MTM2016-77278-P
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Periodic solution ; Limit cycle ; Discontinuous piecewise differential system ; Averaging theory
Published in: Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 4 (April 2019) , p. 1769-1784, ISSN 1531-3492

DOI: 10.3934/dcdsb.2018236


Preprint
17 p, 408.6 KB

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

 Record created 2019-05-16, last modified 2019-06-18



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