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THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS
Cardin, Pedro T.
Da Silva, Paulo R.
Teixeira, Marco A.
Total Authors: 3
 UNESP, Fac Engn Ilha Solteira, Dept Matemat, BR-15385000 Ilha Solteira, SP - Brazil
 UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 S J Rio Preto, SP - Brazil
 Univ Estadual Campinas, IMECC, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 3
QUARTERLY OF APPLIED MATHEMATICS;
Web of Science Citations:
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)