Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type

Maxim S. Shkarayev, Gregor Kovačič, David Cai

Research output: Contribution to journalArticle

Abstract

For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.

Original languageEnglish (US)
Article number036104
JournalPhysical Review E
Volume85
Issue number3
DOIs
StatePublished - Mar 12 2012

Fingerprint

pulse rate
Integrate
pulses
Connectivity
statistics
Statistics
Preferential Attachment
attachment
Scale-free Networks
topology
Pairwise
scaling
Scaling
Topology
Unit

ASJC Scopus subject areas

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

Cite this

Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type. / Shkarayev, Maxim S.; Kovačič, Gregor; Cai, David.

In: Physical Review E, Vol. 85, No. 3, 036104, 12.03.2012.

Research output: Contribution to journalArticle

Shkarayev, Maxim S. ; Kovačič, Gregor ; Cai, David. / Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type. In: Physical Review E. 2012 ; Vol. 85, No. 3.
@article{e7b5beb6047f4e59a9c4f0e2e39b3c59,
title = "Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type",
abstract = "For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.",
author = "Shkarayev, {Maxim S.} and Gregor Kovačič and David Cai",
year = "2012",
month = "3",
day = "12",
doi = "10.1103/PhysRevE.85.036104",
language = "English (US)",
volume = "85",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type

AU - Shkarayev, Maxim S.

AU - Kovačič, Gregor

AU - Cai, David

PY - 2012/3/12

Y1 - 2012/3/12

N2 - For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.

AB - For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.

UR - http://www.scopus.com/inward/record.url?scp=84858233360&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858233360&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.85.036104

DO - 10.1103/PhysRevE.85.036104

M3 - Article

VL - 85

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 - 3

M1 - 036104

ER -