How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior?

G. M. Ramírez Ávila, J. Kurths, J. L. Guisset, J. L. Deneuborg

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We studied synchronization and clustering in two types of pulse-coupled oscillators, namely, integrate-and-fire and light-controlled oscillators. We considered for the analysis globally coupled oscillators, either by a mean-field type coupling or a distance-dependent one. Using statistically diverse measures such as the transient, probability of total synchronization, fraction of clustered oscillators, mean size, and mean number of clusters, we describe clustering and synchronous behavior for populations of nonidentical oscillators and perform a comparative analysis of the behavioral differences and similitudes among these types of oscillators. Considering a mean-field approach, we found high probability of total synchronization in all cases for integrate-and-fire oscillators; on the other hand, in a more realistic situation, for light-controlled oscillators, i.e., when oscillators do not fire instantaneously, the probability of total synchronization decreases drastically for small differences among the oscillators and subsequently, for larger differences, it slightly increases. When the coupling strength depends on the distance, the probability of total synchronization plummets dramatically with the number of oscillators especially in the case of integrate-and-fire oscillators. The latter constitutes an interesting result because it indicates that in realistic situations, the probability of total synchronization is not very high for a population of pulse-coupled oscillators; this entails that its utilization as a paradigmatic model of total synchronization does not suit well, especially when the coupling depends on the distance. This article is dedicated to our good friend and colleague Hilda Cerdeira as a tribute to the scientific work developed over her career.
Original languageEnglish
Pages (from-to)2759-2773
Number of pages15
JournalThe European Physical Journal. Special Topics
Volume223
Issue number13
Early online date10 Dec 2014
DOIs
Publication statusPublished - Dec 2014

Fingerprint

Synchronization
oscillators
pulses
synchronism
Fires

Cite this

How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior? / Ramírez Ávila, G. M. ; Kurths, J.; Guisset, J. L.; Deneuborg, J. L.

In: The European Physical Journal. Special Topics, Vol. 223, No. 13, 12.2014, p. 2759-2773.

Research output: Contribution to journalArticle

Ramírez Ávila, G. M. ; Kurths, J. ; Guisset, J. L. ; Deneuborg, J. L. / How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior?. In: The European Physical Journal. Special Topics. 2014 ; Vol. 223, No. 13. pp. 2759-2773.
@article{c30f44d554bc44a18dd711d3f3185342,
title = "How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior?",
abstract = "We studied synchronization and clustering in two types of pulse-coupled oscillators, namely, integrate-and-fire and light-controlled oscillators. We considered for the analysis globally coupled oscillators, either by a mean-field type coupling or a distance-dependent one. Using statistically diverse measures such as the transient, probability of total synchronization, fraction of clustered oscillators, mean size, and mean number of clusters, we describe clustering and synchronous behavior for populations of nonidentical oscillators and perform a comparative analysis of the behavioral differences and similitudes among these types of oscillators. Considering a mean-field approach, we found high probability of total synchronization in all cases for integrate-and-fire oscillators; on the other hand, in a more realistic situation, for light-controlled oscillators, i.e., when oscillators do not fire instantaneously, the probability of total synchronization decreases drastically for small differences among the oscillators and subsequently, for larger differences, it slightly increases. When the coupling strength depends on the distance, the probability of total synchronization plummets dramatically with the number of oscillators especially in the case of integrate-and-fire oscillators. The latter constitutes an interesting result because it indicates that in realistic situations, the probability of total synchronization is not very high for a population of pulse-coupled oscillators; this entails that its utilization as a paradigmatic model of total synchronization does not suit well, especially when the coupling depends on the distance. This article is dedicated to our good friend and colleague Hilda Cerdeira as a tribute to the scientific work developed over her career.",
author = "{Ram{\'i}rez {\'A}vila}, {G. M.} and J. Kurths and Guisset, {J. L.} and Deneuborg, {J. L.}",
year = "2014",
month = "12",
doi = "10.1140/epjst/e2014-02290-y",
language = "English",
volume = "223",
pages = "2759--2773",
journal = "The European Physical Journal. Special Topics",
issn = "1951-6355",
publisher = "SPRINGER HEIDELBERG",
number = "13",

}

TY - JOUR

T1 - How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior?

AU - Ramírez Ávila, G. M.

AU - Kurths, J.

AU - Guisset, J. L.

AU - Deneuborg, J. L.

PY - 2014/12

Y1 - 2014/12

N2 - We studied synchronization and clustering in two types of pulse-coupled oscillators, namely, integrate-and-fire and light-controlled oscillators. We considered for the analysis globally coupled oscillators, either by a mean-field type coupling or a distance-dependent one. Using statistically diverse measures such as the transient, probability of total synchronization, fraction of clustered oscillators, mean size, and mean number of clusters, we describe clustering and synchronous behavior for populations of nonidentical oscillators and perform a comparative analysis of the behavioral differences and similitudes among these types of oscillators. Considering a mean-field approach, we found high probability of total synchronization in all cases for integrate-and-fire oscillators; on the other hand, in a more realistic situation, for light-controlled oscillators, i.e., when oscillators do not fire instantaneously, the probability of total synchronization decreases drastically for small differences among the oscillators and subsequently, for larger differences, it slightly increases. When the coupling strength depends on the distance, the probability of total synchronization plummets dramatically with the number of oscillators especially in the case of integrate-and-fire oscillators. The latter constitutes an interesting result because it indicates that in realistic situations, the probability of total synchronization is not very high for a population of pulse-coupled oscillators; this entails that its utilization as a paradigmatic model of total synchronization does not suit well, especially when the coupling depends on the distance. This article is dedicated to our good friend and colleague Hilda Cerdeira as a tribute to the scientific work developed over her career.

AB - We studied synchronization and clustering in two types of pulse-coupled oscillators, namely, integrate-and-fire and light-controlled oscillators. We considered for the analysis globally coupled oscillators, either by a mean-field type coupling or a distance-dependent one. Using statistically diverse measures such as the transient, probability of total synchronization, fraction of clustered oscillators, mean size, and mean number of clusters, we describe clustering and synchronous behavior for populations of nonidentical oscillators and perform a comparative analysis of the behavioral differences and similitudes among these types of oscillators. Considering a mean-field approach, we found high probability of total synchronization in all cases for integrate-and-fire oscillators; on the other hand, in a more realistic situation, for light-controlled oscillators, i.e., when oscillators do not fire instantaneously, the probability of total synchronization decreases drastically for small differences among the oscillators and subsequently, for larger differences, it slightly increases. When the coupling strength depends on the distance, the probability of total synchronization plummets dramatically with the number of oscillators especially in the case of integrate-and-fire oscillators. The latter constitutes an interesting result because it indicates that in realistic situations, the probability of total synchronization is not very high for a population of pulse-coupled oscillators; this entails that its utilization as a paradigmatic model of total synchronization does not suit well, especially when the coupling depends on the distance. This article is dedicated to our good friend and colleague Hilda Cerdeira as a tribute to the scientific work developed over her career.

U2 - 10.1140/epjst/e2014-02290-y

DO - 10.1140/epjst/e2014-02290-y

M3 - Article

VL - 223

SP - 2759

EP - 2773

JO - The European Physical Journal. Special Topics

JF - The European Physical Journal. Special Topics

SN - 1951-6355

IS - 13

ER -