Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots

André Bergner, M Carmen Romano, Jurgen Kurths, Marco Thiel

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We present a method for synchronization analysis, that is able to handle large networks of interacting dynamical units. We focus on large networks with different topologies (random, small-world and scale-free) and neuronal dynamics at each node. We consider neurons that exhibit dynamics on two time scales, namely spiking and bursting behavior. The proposed method is able to distinguish between synchronization of spikes and synchronization of bursts, so that we analyze the synchronization of each time scale separately. We find for all network topologies that the synchronization of the bursts sets in for smaller coupling strengths than the synchronization of the spikes. Furthermore, we obtain an interesting behavior for the synchronization of the spikes dependent on the coupling strength: for small values of the coupling, the synchronization of the spikes increases, but for intermediate values of the coupling, the synchronization index of the spikes decreases. For larger values of the coupling strength, the synchronization index increases again until all the spikes synchronize.
Original languageEnglish
Title of host publicationLectures in Supercomputational Neurosciences
Subtitle of host publicationDynamics in Complex Brain Networks
EditorsPeter beim Graben, Changsong Zhou, Marco Thiel, Jurgen Kurths
Place of PublicationBerlin, Germany
PublisherSpringer Science+Business Media
Pages177-191
Number of pages15
ISBN (Electronic)9783540731597
ISBN (Print)354073158X, 9783540731580
DOIs
Publication statusPublished - 20 Dec 2007

Publication series

NameUnderstanding Complex Systems
PublisherSpringer Science+Business Media
ISSN (Print)1860-0832

Fingerprint

synchronism
plots
spikes
bursts
topology
spiking
neurons

Cite this

Bergner, A., Romano, M. C., Kurths, J., & Thiel, M. (2007). Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots. In P. beim Graben, C. Zhou, M. Thiel, & J. Kurths (Eds.), Lectures in Supercomputational Neurosciences: Dynamics in Complex Brain Networks (pp. 177-191). (Understanding Complex Systems). Berlin, Germany: Springer Science+Business Media. https://doi.org/10.1007/978-3-540-73159-7_6

Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots. / Bergner, André; Romano, M Carmen; Kurths, Jurgen; Thiel, Marco.

Lectures in Supercomputational Neurosciences: Dynamics in Complex Brain Networks. ed. / Peter beim Graben; Changsong Zhou; Marco Thiel; Jurgen Kurths. Berlin, Germany : Springer Science+Business Media, 2007. p. 177-191 (Understanding Complex Systems).

Research output: Chapter in Book/Report/Conference proceedingChapter

Bergner, A, Romano, MC, Kurths, J & Thiel, M 2007, Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots. in P beim Graben, C Zhou, M Thiel & J Kurths (eds), Lectures in Supercomputational Neurosciences: Dynamics in Complex Brain Networks. Understanding Complex Systems, Springer Science+Business Media, Berlin, Germany, pp. 177-191. https://doi.org/10.1007/978-3-540-73159-7_6
Bergner A, Romano MC, Kurths J, Thiel M. Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots. In beim Graben P, Zhou C, Thiel M, Kurths J, editors, Lectures in Supercomputational Neurosciences: Dynamics in Complex Brain Networks. Berlin, Germany: Springer Science+Business Media. 2007. p. 177-191. (Understanding Complex Systems). https://doi.org/10.1007/978-3-540-73159-7_6
Bergner, André ; Romano, M Carmen ; Kurths, Jurgen ; Thiel, Marco. / Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots. Lectures in Supercomputational Neurosciences: Dynamics in Complex Brain Networks. editor / Peter beim Graben ; Changsong Zhou ; Marco Thiel ; Jurgen Kurths. Berlin, Germany : Springer Science+Business Media, 2007. pp. 177-191 (Understanding Complex Systems).
@inbook{db123a5c66634fc19fa9e071e975164d,
title = "Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots",
abstract = "We present a method for synchronization analysis, that is able to handle large networks of interacting dynamical units. We focus on large networks with different topologies (random, small-world and scale-free) and neuronal dynamics at each node. We consider neurons that exhibit dynamics on two time scales, namely spiking and bursting behavior. The proposed method is able to distinguish between synchronization of spikes and synchronization of bursts, so that we analyze the synchronization of each time scale separately. We find for all network topologies that the synchronization of the bursts sets in for smaller coupling strengths than the synchronization of the spikes. Furthermore, we obtain an interesting behavior for the synchronization of the spikes dependent on the coupling strength: for small values of the coupling, the synchronization of the spikes increases, but for intermediate values of the coupling, the synchronization index of the spikes decreases. For larger values of the coupling strength, the synchronization index increases again until all the spikes synchronize.",
author = "Andr{\'e} Bergner and Romano, {M Carmen} and Jurgen Kurths and Marco Thiel",
year = "2007",
month = "12",
day = "20",
doi = "10.1007/978-3-540-73159-7_6",
language = "English",
isbn = "354073158X",
series = "Understanding Complex Systems",
publisher = "Springer Science+Business Media",
pages = "177--191",
editor = "{beim Graben}, Peter and Changsong Zhou and Marco Thiel and Jurgen Kurths",
booktitle = "Lectures in Supercomputational Neurosciences",

}

TY - CHAP

T1 - Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots

AU - Bergner, André

AU - Romano, M Carmen

AU - Kurths, Jurgen

AU - Thiel, Marco

PY - 2007/12/20

Y1 - 2007/12/20

N2 - We present a method for synchronization analysis, that is able to handle large networks of interacting dynamical units. We focus on large networks with different topologies (random, small-world and scale-free) and neuronal dynamics at each node. We consider neurons that exhibit dynamics on two time scales, namely spiking and bursting behavior. The proposed method is able to distinguish between synchronization of spikes and synchronization of bursts, so that we analyze the synchronization of each time scale separately. We find for all network topologies that the synchronization of the bursts sets in for smaller coupling strengths than the synchronization of the spikes. Furthermore, we obtain an interesting behavior for the synchronization of the spikes dependent on the coupling strength: for small values of the coupling, the synchronization of the spikes increases, but for intermediate values of the coupling, the synchronization index of the spikes decreases. For larger values of the coupling strength, the synchronization index increases again until all the spikes synchronize.

AB - We present a method for synchronization analysis, that is able to handle large networks of interacting dynamical units. We focus on large networks with different topologies (random, small-world and scale-free) and neuronal dynamics at each node. We consider neurons that exhibit dynamics on two time scales, namely spiking and bursting behavior. The proposed method is able to distinguish between synchronization of spikes and synchronization of bursts, so that we analyze the synchronization of each time scale separately. We find for all network topologies that the synchronization of the bursts sets in for smaller coupling strengths than the synchronization of the spikes. Furthermore, we obtain an interesting behavior for the synchronization of the spikes dependent on the coupling strength: for small values of the coupling, the synchronization of the spikes increases, but for intermediate values of the coupling, the synchronization index of the spikes decreases. For larger values of the coupling strength, the synchronization index increases again until all the spikes synchronize.

U2 - 10.1007/978-3-540-73159-7_6

DO - 10.1007/978-3-540-73159-7_6

M3 - Chapter

SN - 354073158X

SN - 9783540731580

T3 - Understanding Complex Systems

SP - 177

EP - 191

BT - Lectures in Supercomputational Neurosciences

A2 - beim Graben, Peter

A2 - Zhou, Changsong

A2 - Thiel, Marco

A2 - Kurths, Jurgen

PB - Springer Science+Business Media

CY - Berlin, Germany

ER -