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)

Data:	2019
Resum:	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.
Ajuts:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2016-77278-P
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Periodic solution ; Limit cycle ; Discontinuous piecewise differential system ; Averaging theory
Publicat a:	Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 4 (April 2019) , p. 1769-1784, ISSN 1553-524X

DOI: 10.3934/dcdsb.2018236

Postprint 17 p, 408.6 KB

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