Cross-scale excitability in networks of quadratic integrate-and-fire neurons

Authors

D. Avitabile, M. Desroches, G. Bard Ermentrout

Abstract

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanisms of excitability in an infinite heterogeneous population of coupled quadratic integrate and fire (QIF) cells maintains echoes of the mechanism for the individual components. We exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical and numerical analysis to develop a novel and comprehensive framework for excitability in large populations.

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BibTeX‌

@unpublished{avitabile:hal-03326530,
  TITLE = {{Cross-scale excitability in networks of quadratic integrate-and-fire neurons}},
  AUTHOR = {Avitabile, Daniele and Desroches, Mathieu and Bard Ermentrout, G},
  URL = {https://hal.inria.fr/hal-03326530},
  NOTE = {working paper or preprint},
  YEAR = {2021},
  MONTH = Aug,
  KEYWORDS = {canards ; Ott-Antonsen ansatz ; QIF neurons ; slow-fast dynamics ; bursting ; mean-field limit},
  PDF = {https://hal.inria.fr/hal-03326530/file/ade.pdf},
  HAL_ID = {hal-03326530},
  HAL_VERSION = {v1},
}