Bursting is one of the fundamental rhythms that excitable cells can generate either in
response to incoming stimuli or intrinsically. It has been a topic of intense research in …

Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are
pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics …

The mechanism of compound bursting behaviors of a forced Mathieu-van der Pol-Duffing
system is explored. Four compound bursting types and one typical relaxation oscillation, ie …

In this paper, we present two bursting patterns induced by pulse-shaped explosion (PSE)
and two bursting patterns triggered by non-PSE based upon a van der Pol-Mathieu oscillator …

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 document we review a geometric technique, called\emph {the blow-up method}, as it
has been used to analyze and understand the dynamics of fast-slow systems around non …

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 …

This paper provides the classification of the phase portraits in the Poincaré disc of all
piecewise linear continuous differential systems with two zones separated by a straight line …

For the predator-prey model with the sigmoid functional response whose denominator has
no real roots, the dynamics has already been characterized. Whereas, when the …

This paper investigates the complex bursting behaviors of the cubic-quintic Duffing-van der
Pol system with two slow-varying forcing periodic excitations. Four novel bursting patterns …