This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

We use blowup to study the regularization of codimension-one two-fold singularities in
planar piecewise smooth (PWS) dynamical systems. We focus on singular canards …

We study the regularization of an oriented 1-foliation F on M∖ Σ where M is a smooth
manifold and Σ⊂ M is a closed subset, which can be interpreted as the discontinuity locus of …

A piecewise-smooth second-order singularly perturbed differential equation whose right-
hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a …

This paper investigates a two-point boundary value problem for a second-order singularly
perturbed ordinary differential equation in the case of multiple roots of the degenerate …

One of the most common hypotheses on the theory of non-smooth dynamical systems is a
regular surface as switching manifold, at which case there is at least well-defined and …

This paper studies a particular type of planar Filippov system that consists of two
discontinuity boundaries separating the phase plane into three disjoint regions with different …

We consider piecewise smooth vector fields (PSVF) defined in open sets M ⊆ R^ n M⊆ R n
with switching manifold being a smooth surface Σ Σ. We assume that M ∖ Σ M\Σ contains …

Choosing. The methods are based on the geometric singular perturbation (GSP, for short)
approach, Melnikov method and invariant manifolds theory. Interestingly, not only the explicit …

A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary
equation of reaction-diffusion-advection type is studied. A new class of problems in the case …