Slow–fast systems and sliding on codimension 2 switching manifolds. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: da Silva, Paulo Ricardo; Nunes, Willian Pereira
• Is Part Of: Dynamical systems. Volume 34:Issue 4(2019)
• Page Start: 613
• Page End: 639
• Publication Date: 2019-10-02
• Subjects: Singular perturbation -- non-smooth systems -- invariant manifolds -- Hopf bifurcation -- Bogdanov–Takens bifurcation; 34D15 -- 34C45 -- 34C07 -- 34C23 -- 34C25; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1579782
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this work, we consider piecewise smooth vector fields X defined in R n ∖ Σ, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε . η, ε, η > 0, satisfying that X ε, η converges uniformly to X in each compact subset of R n ∖Σ when ε, η → 0 . We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of X ε . η . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.