Three time scale singular perturbation problems and nonsmooth dynamical systems

• Autor(a) principal: Cardin, Pedro T. [UNESP]
• Data de Publicação: 2014
• Outros Autores: da Silva, Paulo R. [UNESP], Teixeira, Marco A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1090/S0033-569X-2014-01360-X; http://hdl.handle.net/11449/171750

In this paper we study three time scale singular perturbation problems where x = (x, y, z) ∈ Rn × Rm × Rp, ε and δ are two independent small parameters (0 < ε, δ ≪ 1), and f, g, h are Cr functions, where r is big enough for our purposes. We establish conditions for the existence of compact invariant sets (singular points, periodic and homoclinic orbits) when ε, δ > 0. Our main strategy is to consider three time scales which generate three different limit problems. In addition, we prove that double regularization of nonsmooth dynamical systems with self-intersecting switching variety provides a class of three time scale singular perturbation problems.