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 …

Regime shifts are substantial, long‐lasting reorganizations of complex systems, such as
ecosystems. Large ecosystem changes such as eutrophication, shifts among vegetation …

Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-
away attractors. The terms “critical transition” or “tip** point” have been used to describe …

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 …

A detailed numerical investigation of pattern selection for thermocapillary flow in rectangular
containers in microgravity is presented. These dynamics are studied for liquid n-octadecane …

The purpose of this paper aims to explore the mechanism of several different periodic
bursting patterns based on a Mathieu-van der Pol-Duffing energy harvester with parameter …

Critical transitions occur in a wide variety of applications including mathematical biology,
climate change, human physiology and economics. Therefore it is highly desirable to find …

We study the stochastic FitzHugh–Nagumo equations, modelling the dynamics of neuronal
action potentials in parameter regimes characterized by mixed-mode oscillations. The …

We consider slow–fast systems of differential equations, in which both the slow and fast
variables are perturbed by noise. When the deterministic system admits a uniformly …

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, ie, the
different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the …