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

Elizabeth N Davison; Zahra Aminzare; Biswadip Dey; Naomi Ehrich Leonard

doi:10.1063/1.5050178

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

Journal article

Open access

Peer reviewed

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

Elizabeth N Davison, Zahra Aminzare, Biswadip Dey and Naomi Ehrich Leonard

Chaos (Woodbury, N.Y.), Vol.29(3), pp.033105-033105

03/2019

DOI: 10.1063/1.5050178

PMID: 30927863

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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.

Action Potentials - physiology

Models, Neurological

Brain - physiology

Nerve Net - physiology

Computer Simulation

Neurons - physiology

Details

Title: Subtitle: Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons
Creators: Elizabeth N Davison - Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
Zahra Aminzare - Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA
Biswadip Dey - Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
Naomi Ehrich Leonard - Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08540, USA
Resource Type: Journal article
Publication Details: Chaos (Woodbury, N.Y.), Vol.29(3), pp.033105-033105
DOI: 10.1063/1.5050178
PMID: 30927863
NLM abbreviation: Chaos
ISSN: 1054-1500
eISSN: 1089-7682
Publisher: United States
Grant note: DOI: 10.13039/100000001, name: National Science Foundation, award: DGE-1656466, DMS-1430077; DOI: 10.13039/100000006, name: Office of Naval Research, award: N00014-14-1-0635
Language: English
Date published: 03/2019
Academic Unit: Iowa Neuroscience Institute; Mathematics
Record Identifier: 9983985914902771

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