In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …

In this document we review a geometric technique, called\emph {the blow-up method}, as it
has been used to analyze and understand the dynamics of fast-slow systems around non …

We propose a mathematical formalism for discrete multi-scale dynamical systems induced
by maps which parallels the established geometric singular perturbation theory for …

We consider a fast-slow partial differential equation (PDE) with reaction-diffusion dynamics
in the fast variable and the slow variable driven by a differential operator on a bounded …

We study dynamic networks under an undirected consensus communication protocol and
with one state-dependent weighted edge. We assume that the aforementioned dynamic …

In this work we study the Brusselator--a prototypical model for chemical oscillations--under
the assumption that the bifurcation parameter is of order $ O (1/\epsilon) $ for positive …

In this paper we analyse the phenomenon of the slow passage through a transcritical
bifurcation with special emphasis in the maximal delay zd (λ, ɛ) as a function of the …

We study a singularly perturbed fast-slow system of two partial differential equations (PDEs)
of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume that …

We study fast-slow maps obtained by discretization of planar fast-slow systems in
continuous time. We focus on describing the so-called delayed loss of stability induced by …

Canards are a well-studied phenomenon in fast-slow ordinary differential equations
implying the delayed loss of stability after the slow passage through a singularity. Recent …