Regularization of piecewise smooth singularly perturbed systems

Pedro Toniol Cardin, Jaime Rezende de Moraes, Paulo Ricardo da Silva

Resumo


In this work we deal with piecewise smooth singularly perturbed systems

{ F (x, y, ε)   if   h(x, y, ε) 0,

x˙ =

εy˙ = H(x, y, ε).                     (1)

G(x, y, ε)   if   h(x, y, ε) 0, 

In system (1), ε R is a non-negative small parameter, x Rn and y R denote the slow and fast variables, respectively, and F , G, h and H are Cr maps which vary differentially with respect to ε, with r 1. We study the Sotomayor–Teixeira regularization of periodic orbits of system (1) with ε = 0 and with ε > 0 sufficiently small. More specifically, we establish the persistence of periodic orbits with sewing or with sliding of system (1) with ε = 0 and with ε > 0 for their respective regularized systems.


Palavras-chave


Singular perturbation, Filippov systems, regularization.

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DOI: https://doi.org/10.5540/03.2015.003.02.0011

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