Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons

TL;DR

This paper investigates the complex dynamics of coupled FitzHugh-Nagumo neurons, revealing bifurcation structures, conditions for mixed mode oscillations, and phase locking in networks with heterogeneous inputs.

Contribution

It provides a detailed bifurcation analysis and necessary conditions for mixed mode oscillations and phase locking in coupled neuron models, extending to larger networks.

Findings

Identified bifurcation structures leading to mixed mode oscillations.

Derived necessary conditions for canard solutions in coupled neurons.

Established sufficient conditions for phase locking in heterogeneous networks.

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.