59 citations · 138 across the 20 of their papers we have counts for
5 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…
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…
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…
Canards, folded nodes and mixed-mode oscillations in piecewise-linear slow-fast systems
Mathieu Desroches, Antoni Guillamon, Enrique Ponce +3
Canard-induced phenomena have been extensively studied in the last three decades, both from the mathematical and from the application viewpoints. Canards in slow-fast systems with…
A method for the reconstruction of unknown non-monotonic growth functions in the chemostat
Jan Sieber, Alain Rapaport, Serafim Rodrigues +1
We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the gro…