On non-smooth slow-fast systems

2018/09/20 by Jaime Resende de Moraes, de Moraes, Jaime Resende, Paulo Ricardo da Silva +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1809.07612

arxiv created 2018/09/20 · arxiv updated 2018/09/21

Abstract

We deal with non-smooth differential systems z=X(z), z∈ Rⁿ, with discontinuity occurring in a codimension one smooth surface Σ. A regularization of X is a 1-parameter family of smooth vector fields X^δ,δ>0, satisfying that X^δ converges pointwise to X in Rⁿ∖Σ, when δ→ 0. We work with two known regularizations: the classical one proposed by Sotomayor and Teixeira and its generalization, using non-monotonic transition functions. Using the techniques of geometric singular perturbation theory we study minimal sets of regularized systems. Moreover, non-smooth slow-fast systems are studied and the persistence of the sliding region by singular perturbations is analyzed.

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