Per citar aquest document: http://ddd.uab.cat/record/145326
Scopus: 3 cites, Web of Science: 3 cites,
Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2015
Resum: Let p be a uniform isochronous cubic polynomial center. We study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively, when they are perturbed, either inside the class of all continuous cubic polynomial differential systems, or inside the class of all discontinuous differential systems formed by two cubic differential systems separated by the straight line y = 0. In the case of continuous perturbations using the averaging theory of order 6 we show that the maximum number of small limit cycles that can appear in a Hopf bifurcation at p is 3, and this number can be reached. For a subfamily of these systems using the averaging theory of first order we prove that at most 3 medium limit cycles can bifurcate from the periodic solutions surrounding p, and this number can be reached. In the case of discontinuous perturbations using the averaging theory of order 6 we prove that the maximum number of small limit cycles that can appear in a Hopf bifurcation at p is 5, and this number can be reached. For a subfamily of these systems using the averaging method of first order we show that the maximum number of medium limit cycles that can bifurcate from the periodic solutions surrounding p is 7, and this number can be reached. We also provide all the first integrals and the phase portraits in the Poincar´e disc for the uniform isochronous cubic centers.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Averaging theory ; Limit cycles ; Periodic orbit ; Polynomial vector field ; Uniform isochronous center
Publicat a: Journal of Computational and Applied Mathematics, Vol. 277 (2015) , p. 171-191, ISSN 0377-0427

DOI: 10.1016/j.cam.2014.09.007


36 p, 790.3 KB

El registre apareix a les col·leccions:
Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
Articles > Articles publicats

 Registre creat el 2016-01-12, darrera modificació el 2017-01-16



   Favorit i Compartir