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 …

The chapter is devoted to the investigation of the relationship between slow integral
manifolds of singularly perturbed differential equations and critical phenomena in chemical …

Ordinary differential equations (ODEs) are the preferred language for the investigation and
understanding of various natural phenomena. Employed extensively in natural sciences …

Canard-induced phenomena have been extensively studied in the last three decades, from
both the mathematical and the application viewpoints. Canards in slow-fast systems with (at …

We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits
limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive …

In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due
to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth …

The paper investigates the relaxation oscillations of a classical predator–prey model, based
on the natural ecological assumption that the maximum per capita birth rate of the predator …

In this article we analyze n-dimensional slow–fast systems in a piecewise linear framework.
In particular, we prove a Fenichel's-like Theorem where we give an explicit expression for …

In this work, we analyze the existence and stability of canard solutions in a class of planar
piecewise linear systems with three zones, using a singular perturbation theory approach …

This paper concerns systems of ODEs that are continuous, piecewise-linear (with two
pieces) and slow-fast. The limiting slow dynamics occurs on a piecewise-linear critical …