THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS

Autor(es)

Cardin, Pedro T. ^[1] ; Da Silva, Paulo R. ^[2] ; Teixeira, Marco A. ^[3]

Afiliação do(s) autor(es)

^[1] UNESP, Fac Engn Ilha Solteira, Dept Matemat, BR-15385000 Ilha Solteira, SP - Brazil

^[2] UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 S J Rio Preto, SP - Brazil

^[3] Univ Estadual Campinas, IMECC, BR-13081970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: QUARTERLY OF APPLIED MATHEMATICS; v. 72, n. 4, p. 673-687, 2014.
• Citações Web of Science: 3

Resumo

In this paper we study three time scale singular perturbation problems epsilon x ` = f(x, epsilon, delta), y ` = g(x, epsilon, delta), z ` = delta h(x, delta, delta), where x = (x, y, z) is an element of R-n x R-m x R-p, epsilon and delta are two independent small parameters (0 < epsilon, delta << 1), and f, g, h are C-r 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 epsilon, delta > 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. (AU)

• Processo FAPESP: 13/21947-6 - Teoria geométrica das equações diferenciais perturbadas singularmente
• Beneficiário: Pedro Toniol Cardin
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático