Emergence of spatially periodic diffusive waves in small-world neuronal networks

Qinglong L. Gu, Yanyang Xiao, Songting Li, Doug Zhou

Research output: Contribution to journalArticle

Abstract

It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

Original languageEnglish (US)
Article number042401
JournalPhysical Review E
Volume100
Issue number4
DOIs
StatePublished - Oct 1 2019

Fingerprint

Neuronal Network
Small-world Network
Network Dynamics
Small World
Gratings
Attractor
Neuron
Lattice Dynamics
Simulation Analysis
Spatial Distribution
Numerical Analysis
Theoretical Analysis
neurons
Siméon Denis Poisson
Integrate
Entire
Numerical Simulation
gratings
Approximation
Demonstrate

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Emergence of spatially periodic diffusive waves in small-world neuronal networks. / Gu, Qinglong L.; Xiao, Yanyang; Li, Songting; Zhou, Doug.

In: Physical Review E, Vol. 100, No. 4, 042401, 01.10.2019.

Research output: Contribution to journalArticle

Gu, Qinglong L. ; Xiao, Yanyang ; Li, Songting ; Zhou, Doug. / Emergence of spatially periodic diffusive waves in small-world neuronal networks. In: Physical Review E. 2019 ; Vol. 100, No. 4.
@article{72e4caca4f474203a0c4f4722b460281,
title = "Emergence of spatially periodic diffusive waves in small-world neuronal networks",
abstract = "It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.",
author = "Gu, {Qinglong L.} and Yanyang Xiao and Songting Li and Doug Zhou",
year = "2019",
month = "10",
day = "1",
doi = "10.1103/PhysRevE.100.042401",
language = "English (US)",
volume = "100",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Emergence of spatially periodic diffusive waves in small-world neuronal networks

AU - Gu, Qinglong L.

AU - Xiao, Yanyang

AU - Li, Songting

AU - Zhou, Doug

PY - 2019/10/1

Y1 - 2019/10/1

N2 - It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

AB - It has been observed in experiment that the anatomical structure of neuronal networks in the brain possesses the feature of small-world networks. Yet how the small-world structure affects network dynamics remains to be fully clarified. Here we study the dynamics of a class of small-world networks consisting of pulse-coupled integrate-and-fire (I&F) neurons. Under stochastic Poisson drive, we find that the activity of the entire network resembles diffusive waves. To understand its underlying mechanism, we analyze the simplified regular-lattice network consisting of firing-rate-based neurons as an approximation to the original I&F small-world network. We demonstrate both analytically and numerically that, with strongly coupled connections, in the absence of noise, the activity of the firing-rate-based regular-lattice network spatially forms a static grating pattern that corresponds to the spatial distribution of the firing rate observed in the I&F small-world neuronal network. We further show that the spatial grating pattern with different phases comprise the continuous attractor of both the I&F small-world and firing-rate-based regular-lattice network dynamics. In the presence of input noise, the activity of both networks is perturbed along the continuous attractor, which gives rise to the diffusive waves. Our numerical simulations and theoretical analysis may potentially provide insights into the understanding of the generation of wave patterns observed in cortical networks.

UR - http://www.scopus.com/inward/record.url?scp=85073072771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073072771&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.100.042401

DO - 10.1103/PhysRevE.100.042401

M3 - Article

AN - SCOPUS:85073072771

VL - 100

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 042401

ER -