Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are
pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics …

In this chapter, we review the most fundamental phenomena in differentiable, finite-
dimensional multiple-time-scale systems as well as the geometric singular perturbation …

Boundary equilibria bifurcation (BEB) arises in piecewise-smooth (PWS) systems when an
equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed …

In this paper, we describe a novel type of relaxation oscillations occurring in a model of
substrate-depletion oscillators. Using geometric singular perturbation theory, with blow-up …

In this paper, we extend the slow divergence-integral from slow-fast systems, due to De
Maesschalck, Dumortier and Roussarie, to smooth systems that limit onto piecewise smooth …

The classical Painlevé paradox consists of a slender rigid rod slip** on a rigid rough
surface. If the coefficient of friction μ is high enough, the governing equations predict that the …

Singular exponential nonlinearities of the form eh (x) ϵ-1 with ϵ> 0 small occur in many
different applications. These terms have essential singularities for ϵ= 0 leading to very …

In mechanics, one often describes microscopic processes such as those leading to friction
between relative interfaces using macroscopic variables (relative velocity, temperature, etc.) …

We prove the existence of a family of traveling wave solutions in a variant of the Zeldovich–
Frank-Kamenetskii (ZFK) equation, a reaction-diffusion equation which models the …

Recently, concepts from the emerging field of tropical geometry have been used to identify
different scaling regimes in chemical reaction networks where dimension reduction may take …