Speakers
Description
Bursting is a common firing pattern in neurons, characterized by alternating active (spiking) and silent phases. While the transition from tonic spiking to bursting has been widely studied, the mechanisms underlying spike-adding within a burst remain less understood. We investigate spike-adding in a three-dimensional neuronal model with three distinct timescales. Using the FitzHugh–Nagumo system with slow periodic forcing of the voltage equation as a prototypical example, we show that decreasing the forcing frequency and increasing its amplitude induce transitions from single-spike responses to complex bursting with spike-adding. We relate these transitions to folded node and folded saddle singularities in the underlying fast–slow structure. Finally, we demonstrate that similar spike-adding mechanisms arise in the more physiologically realistic Morris–Lecar model.
This work is joint with Pake Melland (Oregon Institute of Technology) and Rodica Curtu (Michigan Technological University) \cite{Melland_ Curtu _ Aminzare _2025}.
Bibliography
@article{Melland_ Curtu _ Aminzare _2025,
author = {Melland, Pake and Curtu, Rodica and Aminzare, Zahra},
title = {Spike-adding Mechanisms in a Three-timescale System: Insights from the Fitzhugh–Nagumo Model with Periodic Forcing},
journal = {SIAM Journal on Applied Dynamical Systems},
volume = {24},
number = {4},
pages = {2977-3011},
year = {2025},
doi = {10.1137/24M1706980},
URL = {https://doi.org/10.1137/24M1706980},
eprint = {https://doi.org/10.1137/24M1706980}}
