59 citations · 222 across the 21 of their papers we have counts for
14 papers · 1 filter
Slow-fast dynamics in a neurotransmitter release model: delayed response to a time-dependent input signal
Mattia Sensi, Mathieu Desroches, Serafim Rodrigues
We propose a generalization of the neurotransmitter release model proposed in \emph{Rodrigues et al. (PNAS, 2016)}. We increase the complexity of the underlying slow-fast system by…
Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons
Daniele Avitabile, Mathieu Desroches, G. Bard Ermentrout
From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In r…
Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach
Halgurd Taher, Daniele Avitabile, Mathieu Desroches
We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that takes short-term synaptic plasticity into account. The one being used here…
Spike-adding and reset-induced canard cycles in adaptive integrate and fire models
Mathieu Desroches, Piotr Kowalczyk, Serafim Rodrigues
We study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation variable on top of membrane potential, and…
Canonical models for torus canards in elliptic bursters
Emre Baspinar, Daniele Avitabile, Mathieu Desroches
We revisit elliptic bursting dynamics from the viewpoint of torus canard solutions. We show that at the transition to and from elliptic burstings, classical or mixed-type torus can…
Towards a new classification of bursting patterns: review & extensions
Mathieu Desroches, John Rinzel, Serafim Rodrigues
The mathematical classification of complex bursting oscillations in multiscale excitable systems, seen for example in physics and neuroscience, has been the subject of active enqui…