This is a book about 'Neurodynamics'. What we mean is that this is a book about how ideas
from dynamical systems theory have been developed and employed in recent years to give …

By applying a singular perturbation approach, canard explosions exhibited by a general
family of singularly perturbed planar Piecewise Linear (PWL) differential systems are …

In this work we deal with the canard regime as a part of a canard explosion taking place in a
PWL version of the van der Pol equation having a flat critical manifold. The proposed …

Multiple-timescale systems often display intricate dynamics, yet of great mathematical
interest and well suited to model real-world phenomena such as bursting oscillations. In the …

We study a class of planar integrate and fire models called adaptive integrate and fire (AIF)
models, which possesses an adaptation variable on top of membrane potential, and whose …

In this chapter we gather recent results on piecewise-linear (PWL) slow-fast dynamical
systems in the canard regime. By focusing on minimal systems in R^ 2 (one slow and one …

The phenomenon of slow passage through a Hopf bifurcation is ubiquitous in multiple-
timescale dynamical systems, where a slowly varying quantity replacing a static parameter …

This paper examines a spike-adding bifurcation phenomenon whereby small-amplitude
canard cycles transition into large-amplitude bursting oscillations along a single continuous …

By applying a singular perturbation approach, canard limit cycles exhibited by a general
family of singularly perturbed planar piecewise linear (PWL) differential systems are …

[eng] n this thesis, we propose a piecewise linear version of the original planar Morris-Lecar
model which we study qualitatively and for which we characterize several bifurcations …