Piecewise-Smooth Slow-Fast Systems

Autor(es)

da Silva, Paulo R. ^[1] ; de Moraes, Jaime R. ^[2]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, Dept Matemat, Inst Biociencias Letras & Ciencias Exatas, Rua C Colombo 2265, BR-15054000 Sao Paulo - Brazil

^[2] Univ Estadual Mato Grosso do Sul, Curso Matemat, Rodovia Dourados Itaum Km 1, BR-79804970 Dourados, MS - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 27, n. 1 MAR 2020.
• Citações Web of Science: 0

Resumo

We deal with piecewise-smooth differential systems (z)over dot = X(z), z = (x, y) is an element of R x Rn-1, with switching occurring in a codimension one smooth surface Sigma. A regularization of X is a 1-parameter family of smooth vector fields X-delta, delta > 0, satisfying that X-delta converges pointwise to X in R-n \textbackslash{} Sigma, when delta -> 0. The regularized system (z)over dot = X-delta(z) is a slow-fast system. We work with two known regularizations: the classical one proposed by Sotomayor and Teixeira and its generalization, using transition functions without imposing the monotonicity condition. Minimal sets of regularized systems are studied with tools of the geometric singular perturbation theory. Moreover, we analyzed the persistence of the sliding region of piecewise-smooth slow-fast systems by singular perturbations. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático