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 …

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

While the stability of present-day reactors is well studied, stability analysis of Generation IV
reactors is in its very beginning. In this paper, the stability of point nuclear reactor models …

We study systems which combine both oscillatory and excitable properties, and hence
intrinsically possess two internal frequencies, responsible for standard spiking and for small …

In this paper, we proposed a fractional-order microscopic chaotic system, derived from a set
of microscopic chemical reactions. The dynamical properties of the proposed model have …

Canards are periodic orbits for which the trajectory follows both the attracting and repelling
parts of a slow manifold. They are associated with a dramatic change in the amplitude and …

The occurrence of spatial domains of large amplitude oscillation on a background of small
amplitude oscillation in a reaction–diffusion system is called localization. We study …

In the present work, we investigate the canard explosion in a van der Pol electronic
oscillator, a fast transition from a small amplitude periodic orbit to a relaxation oscillation. To …

The paper deals with the study of the relation between the Andronov {Hopf bifurcation, the
canard explosion and the critical phenomena for the van der Pol's type system of singularly …

Nonlinear dynamical systems are known to be sensitive to input parameters. In this thesis,
we apply model order reduction to an important class of such systems--one which exhibits …