The dynamics of balanced spiking neuronal networks under poisson drive is not chaotic

Qing Long L. Gu, Zhong Qi K. Tian, Gregor Kovačič, Doug Zhou, David Cai

Research output: Contribution to journalArticle

Abstract

Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the systemwithout the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.

Original languageEnglish (US)
Article number47
JournalFrontiers in Computational Neuroscience
Volume12
DOIs
StatePublished - Jun 28 2018

Fingerprint

Neurons

Keywords

  • Balanced state
  • Chaotic dynamics
  • Delta-pulse coupling
  • Irregular activity
  • Largest Lyapunov exponent

ASJC Scopus subject areas

  • Neuroscience (miscellaneous)
  • Cellular and Molecular Neuroscience

Cite this

The dynamics of balanced spiking neuronal networks under poisson drive is not chaotic. / Gu, Qing Long L.; Tian, Zhong Qi K.; Kovačič, Gregor; Zhou, Doug; Cai, David.

In: Frontiers in Computational Neuroscience, Vol. 12, 47, 28.06.2018.

Research output: Contribution to journalArticle

Gu, Qing Long L. ; Tian, Zhong Qi K. ; Kovačič, Gregor ; Zhou, Doug ; Cai, David. / The dynamics of balanced spiking neuronal networks under poisson drive is not chaotic. In: Frontiers in Computational Neuroscience. 2018 ; Vol. 12.
@article{3c4f2921d61a4de9a3c3044d15c86e0e,
title = "The dynamics of balanced spiking neuronal networks under poisson drive is not chaotic",
abstract = "Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the systemwithout the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.",
keywords = "Balanced state, Chaotic dynamics, Delta-pulse coupling, Irregular activity, Largest Lyapunov exponent",
author = "Gu, {Qing Long L.} and Tian, {Zhong Qi K.} and Gregor Kovačič and Doug Zhou and David Cai",
year = "2018",
month = "6",
day = "28",
doi = "10.3389/fncom.2018.00047",
language = "English (US)",
volume = "12",
journal = "Frontiers in Computational Neuroscience",
issn = "1662-5188",
publisher = "Frontiers Research Foundation",

}

TY - JOUR

T1 - The dynamics of balanced spiking neuronal networks under poisson drive is not chaotic

AU - Gu, Qing Long L.

AU - Tian, Zhong Qi K.

AU - Kovačič, Gregor

AU - Zhou, Doug

AU - Cai, David

PY - 2018/6/28

Y1 - 2018/6/28

N2 - Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the systemwithout the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.

AB - Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the systemwithout the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.

KW - Balanced state

KW - Chaotic dynamics

KW - Delta-pulse coupling

KW - Irregular activity

KW - Largest Lyapunov exponent

UR - http://www.scopus.com/inward/record.url?scp=85049527709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049527709&partnerID=8YFLogxK

U2 - 10.3389/fncom.2018.00047

DO - 10.3389/fncom.2018.00047

M3 - Article

AN - SCOPUS:85049527709

VL - 12

JO - Frontiers in Computational Neuroscience

JF - Frontiers in Computational Neuroscience

SN - 1662-5188

M1 - 47

ER -