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 …

Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an
alternation between oscillations of distinct large and small amplitudes. MMOs have been …

This article concerns the phenomenon of Mixed-Mode Bursting Oscillations (MMBOs). These
are solutions of fast-slow systems of ordinary differential equations that exhibit both small …

Folded saddle-nodes occur generically in one parameter families of singularly perturbed
systems with two slow variables. We show that these folded singularities are the organizing …

We extend canard theory of singularly perturbed systems to the general case of $ k $ slow
and $ m $ fast dimensions, with $ k\ge 2$ and $ m\ge 1$ arbitrary. A folded critical manifold …

This paper investigates mixed-mode oscillations (MMOs) with a three-dimensional
conductance-based cardiac action potential model, which makes the heart beat in a …

Canards are a type of transient dynamics that occur in singularly perturbed systems, and
they are specific types of solutions with varied dynamic behaviours at the boundary region …

Symmetry-breaking in coupled, identical, fast–slow systems produces a rich, dramatic
variety of dynamical behavior—such as amplitudes and frequencies differing by an order of …

This study entails investigation of mixed-mode oscillations (MMOs) with a conductance-
based pyramidal cell (PC) model located in the entorhinal cortex layer V. This six …

Pseudo-plateau bursting is a type of oscillatory waveform associated with mixed mode
dynamics in slow/fast systems and commonly found in neural bursting models. In a recent …