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

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

Research output: Contribution to journalArticle

7 Scopus citations

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

All Science Journal Classification (ASJC) codes

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

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