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Utilize este identificador para citar ou criar um link para este item: http://acervodigital.unesp.br/handle/11449/40445
Título: 
Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems
Autor(es): 
Instituição: 
  • Universidade Estadual Paulista (UNESP)
  • Universidade Estadual de Campinas (UNICAMP)
ISSN: 
0007-4497
Resumo: 
This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.
Data de publicação: 
1-Jun-2012
Citação: 
Bulletin Des Sciences Mathematiques. Paris: Gauthier-villars/editions Elsevier, v. 136, n. 4, p. 444-462, 2012.
Duração: 
444-462
Publicador: 
Gauthier-villars/editions Elsevier
Palavras-chaves: 
  • Regularization
  • Vector fields
  • Singular perturbation
  • Non-smooth vector field
  • Sliding vector field
Fonte: 
http://dx.doi.org/10.1016/j.bulsci.2011.06.001
Endereço permanente: 
Direitos de acesso: 
Acesso restrito
Tipo: 
outro
Fonte completa:
http://repositorio.unesp.br/handle/11449/40445
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