Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons
Abstract
We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.
Keywords
Cite
@article{arxiv.1807.10824,
title = {Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons},
author = {Elizabeth N. Davison and Zahra Aminzare and Biswadip Dey and Naomi Ehrich Leonard},
journal= {arXiv preprint arXiv:1807.10824},
year = {2019}
}