Author(s): da Silva, Paulo R. [UNESP] ; de Moraes, Jaime R.
Date: 2020
Persistent ID: http://hdl.handle.net/11449/200156
Origin: Oasisbr
Subject(s): Invariant manifolds; Periodic solutions; Singular perturbations; Slow and fast motions; Invariant manifolds; Invariant manifolds; Periodic solutions; Periodic solutions; Singular perturbations; Singular perturbations; Slow and fast motions; Slow and fast motions
Made available in DSpace on 2020-12-12T01:59:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01
We deal with piecewise-smooth differential systems ż= X(z) , z= (x, y) ∈ ℝ× ℝn − 1, with switching occurring in a codimension one smooth surface Σ. A regularization of X is a 1-parameter family of smooth vector fields Xδ,δ > 0, satisfying that Xδ converges pointwise to X in ℝn∖ Σ , when δ→ 0. The regularized system ż= Xδ(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.
Departamento de Matemática – Instituto de Biociências Letras e Ciências Exatas UNESP – Univ Estadual Paulista, Rua C. Colombo, 2265
Curso de Matemática – UEMS, Rodovia Dourados–Itaum Km 1
Departamento de Matemática – Instituto de Biociências Letras e Ciências Exatas UNESP – Univ Estadual Paulista, Rua C. Colombo, 2265
