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Two-phase quadratic integrate-and-fire neurons : Exact low-dimensional description for ensembles of finite-voltage neurons

Cestnik, Rok LU (2026) In Physical Review Research 8(1).
Abstract

We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the standard QIF model while producing realistic spike waveforms. Despite this modification, the system retains an exact low-dimensional description in the thermodynamic limit, governed by a single complex Riccati equation. Expressions for collective quantities such as the firing rate and mean voltage remain compact and analytically tractable. Because the formalism preserves the mathematical structure of the standard QIF ensemble, it inherits its many generalizations and can serve as a drop-in replacement... (More)

We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the standard QIF model while producing realistic spike waveforms. Despite this modification, the system retains an exact low-dimensional description in the thermodynamic limit, governed by a single complex Riccati equation. Expressions for collective quantities such as the firing rate and mean voltage remain compact and analytically tractable. Because the formalism preserves the mathematical structure of the standard QIF ensemble, it inherits its many generalizations and can serve as a drop-in replacement in existing mean-field frameworks, providing a more biologically plausible yet still exactly solvable neuronal model.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Research
volume
8
issue
1
article number
L012049
publisher
American Physical Society
external identifiers
  • scopus:105032194834
ISSN
2643-1564
DOI
10.1103/tq4x-8ny1
language
English
LU publication?
yes
id
d3ba1483-5f01-4ff0-8306-36debe65d413
date added to LUP
2026-04-20 10:38:13
date last changed
2026-04-20 10:39:16
@article{d3ba1483-5f01-4ff0-8306-36debe65d413,
  abstract     = {{<p>We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the standard QIF model while producing realistic spike waveforms. Despite this modification, the system retains an exact low-dimensional description in the thermodynamic limit, governed by a single complex Riccati equation. Expressions for collective quantities such as the firing rate and mean voltage remain compact and analytically tractable. Because the formalism preserves the mathematical structure of the standard QIF ensemble, it inherits its many generalizations and can serve as a drop-in replacement in existing mean-field frameworks, providing a more biologically plausible yet still exactly solvable neuronal model.</p>}},
  author       = {{Cestnik, Rok}},
  issn         = {{2643-1564}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Research}},
  title        = {{Two-phase quadratic integrate-and-fire neurons : Exact low-dimensional description for ensembles of finite-voltage neurons}},
  url          = {{http://dx.doi.org/10.1103/tq4x-8ny1}},
  doi          = {{10.1103/tq4x-8ny1}},
  volume       = {{8}},
  year         = {{2026}},
}