The discontinuous matching of two planar linear foci can have three nested crossing limit cycles
Freire, Emilio (Universidad de Sevilla. Escuela Técnica Superior de Ingeniería)
Ponce, Enrique (Universidad de Sevilla. Escuela Técnica Superior de Ingeniería)
Torres, Francisco (Universidad de Sevilla. Escuela Técnica Superior de Ingeniería)

Data:	2014
Resum:	The existence and stability of limit cycles in discontinuous piecewise linear systems obtained by the aggregation of two linear systems of focus type and having only one equilibrium point is considered. By using an adequate canonical form with five parameters, a thorough study of some Poincar'e maps is performed. Different bifurcations which are responsible for the appearance of crossing limit cycles are detected and parameter regions with none, one, two and three crossing limit cycles are found. In particular, a first analytical proof of the existence, for certain differential systems in the considered family, of at least three homotopic crossing limit cycles surrounding the equilibrium point, is included. This fact has recently been numerically discovered in a particular example by S. -M. Huan and X. -S. Yang.
Ajuts:	Ministerio de Economía y Competitividad FEDER/MTM2009-07849
Nota:	This work was partially supported by a MINECO/FEDER grant number MTM2009-07849 and the grant EXC/P08-FQM-03770 of Junta de Andalucía.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Discontinuous piecewise linear systems ; Limit cycles ; Bifurcations
Publicat a:	Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 221-253, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287215
DOI: 10.5565/PUBLMAT_Extra14_13

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