Some techniques to show the existence and uniqueness of limit cycles, typically stated for
smooth vector fields, are extended to continuous piecewise-linear differential systems. New …

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 investigate the mechanism of abrupt transition between small-and large amplitude
oscillations in fast-slow piecewise-linear (PWL) models of FitzHugh–Nagumo (FHN) type. In …

By applying a singular perturbation approach, canard explosions exhibited by a general
family of singularly perturbed planar Piecewise Linear (PWL) differential systems are …

In this work we deal with the canard regime as a part of a canard explosion taking place in a
PWL version of the van der Pol equation having a flat critical manifold. The proposed …

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 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 …

Multiple-timescale systems often display intricate dynamics, yet of great mathematical
interest and well suited to model real-world phenomena such as bursting oscillations. In the …

Hybrid systems often exhibit periodic behaviours. Therefore, the computation and the
stability analysis of hybrid limit cycles is an important problem. Recently, several techniques …

This book illustrates the correlation between connected citizens and smart communities and
cities. It delves into the fundamental element of smart communities, the concept of a unified …