Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems witha a straight line of separation
Llibre, Jaume ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio ![Identificador ORCID](/img/uab/orcid.ico)
(Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
Títol variant: |
On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation |
Data: |
2013 |
Resum: |
In this paper we study the maximum number of limit cycles for planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line. Here we only consider non-sliding limit cycles. For that systems, the interior of any limit cycle only contains a unique singular point or a unique sliding segment. Moreover, the linear differential systems that we consider in every half-plane can have either a focus (F), or a node (N), or a saddle (S), these equilibrium points can be real or virtual. Then, we can consider six kinds of planar discontinuous piecewise linear differential systems: FF, FN, FS, NN, NS, SS. We analyze for each of these types of discontinuous differential systems the maximum number of known limit cycles. |
Ajuts: |
Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
|
Nota: |
El títol de la versió pre-print de l'article és: On the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation |
Nota: |
Agraïments: The second author is partially supported by the FAPESP-BRAZIL grant 2007/06896-5. All the authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC. |
Drets: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Llengua: |
Anglès |
Document: |
Article ; recerca ; Versió acceptada per publicar |
Matèria: |
Non-smooth differential system ;
Limit cycle ;
Piecewise linear differential system |
Publicat a: |
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 4 (2013) , p. 1350066 (10 pages), ISSN 1793-6551 |
DOI: 10.1142/S0218127413500661
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