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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 01, 2019
Source ID
10.1063/1.5050178

Entities

People

  • Biswadip Dey
  • Elizabeth N. Davison
  • Naomi Ehrich Leonard
  • Zahra Aminzare

Organizations

  • National Science Foundation
  • Office of Naval Research
  • Princeton University
  • University of Iowa

Tags

Fields of Study

  • Biology
  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Microwave Engineering.
  • Neural Network Machine Learning.