Artículos de revistas
Piecewise Implicit Differential Systems
Fecha
2017-12-01Registro en:
Journal of Dynamics and Differential Equations, v. 29, n. 4, p. 1519-1537, 2017.
1572-9222
1040-7294
10.1007/s10884-016-9538-2
2-s2.0-84973137389
2-s2.0-84973137389.pdf
Autor
Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
Universidade Federal de São Carlos (UFSCar)
Institución
Resumen
In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form x˙=1,(y˙)2={g1(x,y)ifφ(x,y)≥0g2(x,y)ifφ(x,y)≤0,where g1, g2, φ: U→ R are smooth functions and U⊆ R2 is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form x˙=f(x,y,ε),(εy˙)2=g(x,y,ε)arise when the Sotomayor–Teixeira regularization is applied with (x, y) ∈ U , ε≥ 0 , and f, g smooth in all variables.