Slow–fast systems and sliding on codimension 2 switching manifolds
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In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, 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 \ ∑ 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.
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Bogdanov–Takens bifurcation, Hopf bifurcation, invariant manifolds, non-smooth systems, Singular perturbation
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Inglês
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Dynamical Systems.
