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

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 …

We report a detailed analysis on the emergence of bursting in a recently developed neural
mass model that includes short-term synaptic plasticity. Neural mass models can mimic the …

A vector field is piecewise smooth if its value jumps across a hypersurface, and a two-fold
singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds …

A technique is presented, based on the differential geometry of planar curves, to evaluate
the excitability threshold of neuronal models. The aim is to determine regions of the phase …

In this work we study mixed-mode oscillations in a model of secretion of GnRH
(gonadotropin releasing hormone). The model is a phantom burster consisting of two …

We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits
limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive …

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 …

Neurons can anticipate incoming signals by exploiting a physiological mechanism that is not
well understood. This article offers a novel explanation on how a receiver neuron can predict …

A criterion for the existence of canards in singularly perturbed dynamical systems is
presented. Canards are counterintuitive solutions that evolve along both attracting and …