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 …

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 …

For Markov processes with absorption, we provide general criteria ensuring the existence
and the exponential non-uniform convergence in weighted total variation norm to a quasi …

This paper proposes a novel three-dimensional chaotic system with multiple coexisting
attractors, where different values of a constant control parameter may drive the chaotic …

In this article, we construct and analyse an explicit numerical splitting method for a class of
semi-linear stochastic differential equations (SDEs) with additive noise, where the drift is …

The mechanism of bursting oscillations in high dimensional systems with the coupling of two
scales is an open problem in nonlinear dynamics, since there may coexist stable attractors …

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 …

Identifying early warning signs of sudden population changes and mechanisms leading to
regime shifts are highly desirable in population biology. In this paper, a two-trophic …

We show that the stochastic Morris–Lecar neuron, in a neighborhood of its stable point, can
be approximated by a two-dimensional Ornstein–Uhlenbeck (OU) modulation of a constant …

Quasi-stationary distributions have been used to model the long-term behaviour of
stochastic systems which in some sense terminate, but appear to be stationary over any …