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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Article number033105
JournalChaos
Volume29
Issue number3
DOIs
StatePublished - Mar 1 2019

Fingerprint

Phase Locking
FitzHugh-Nagumo
Mixed Mode
neurons
locking
Neurons
Neuron
Oscillation
oscillations
Model
Canard
Multiple Time Scales
Coupled Model
Complex networks
Complex Networks
Coupled System
brain
Brain
Time Scales
Bifurcation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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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.",
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Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons. / Ehrich Leonard, Naomi.

In: Chaos, Vol. 29, No. 3, 033105, 01.03.2019.

Research output: Contribution to journalArticle

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