On the Interplay of Noise and Delay in Coupled Oscillators

Otti D'Huys, Thomas Jüngling, Wolfgang Kinzel

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Abstract

Coupling delays can play an important role in the dynamics of various networks, such as coupled semiconductor lasers, communication networks, genetic transcription circuits or the brain. A well established effect of a delay is to induce multistability: In oscillatory systems a delay gives rise to coexistent periodic orbits with different frequencies and oscillation patterns. Adding noise to the dynamics, the network switches stochastically between these delay-induced orbits. For phase oscillators, we compute analytically the distribution of frequencies, the robustness to noise and their dependence on system parameters as the coupling strength and coupling delay.
Original languageEnglish
Title of host publicationControl of Self-Organising Nonlinear Systems
EditorsEckehard Schöll, Sabine H. Klapp, Philipp Hövel
PublisherSpringer
Pages127-145
ISBN (Print)978-3-319-28028-8; 978-3-319-28027-1
DOIs
Publication statusPublished - 2016

Publication series

NameUnderstanding Complex Systems Springer Complexity
PublisherSpringer

Fingerprint

oscillators
orbits
communication networks
brain
optical communication
switches
semiconductor lasers
oscillations

Keywords

  • Stochastic dynamic systems
  • time delay
  • coupled systems

Cite this

D'Huys, O., Jüngling, T., & Kinzel, W. (2016). On the Interplay of Noise and Delay in Coupled Oscillators. In E. Schöll, S. H. Klapp, & P. Hövel (Eds.), Control of Self-Organising Nonlinear Systems (pp. 127-145). (Understanding Complex Systems Springer Complexity). Springer. https://doi.org/10.1007/978-3-319-28028-8_7
D'Huys, Otti ; Jüngling, Thomas ; Kinzel, Wolfgang. / On the Interplay of Noise and Delay in Coupled Oscillators. Control of Self-Organising Nonlinear Systems. editor / Eckehard Schöll ; Sabine H. Klapp ; Philipp Hövel. Springer, 2016. pp. 127-145 (Understanding Complex Systems Springer Complexity).
@inbook{4d2a6a31dd124071a47967b584447162,
title = "On the Interplay of Noise and Delay in Coupled Oscillators",
abstract = "Coupling delays can play an important role in the dynamics of various networks, such as coupled semiconductor lasers, communication networks, genetic transcription circuits or the brain. A well established effect of a delay is to induce multistability: In oscillatory systems a delay gives rise to coexistent periodic orbits with different frequencies and oscillation patterns. Adding noise to the dynamics, the network switches stochastically between these delay-induced orbits. For phase oscillators, we compute analytically the distribution of frequencies, the robustness to noise and their dependence on system parameters as the coupling strength and coupling delay.",
keywords = "Stochastic dynamic systems, time delay, coupled systems",
author = "Otti D'Huys and Thomas J{\"u}ngling and Wolfgang Kinzel",
year = "2016",
doi = "10.1007/978-3-319-28028-8_7",
language = "English",
isbn = "978-3-319-28028-8; 978-3-319-28027-1",
series = "Understanding Complex Systems Springer Complexity",
publisher = "Springer",
pages = "127--145",
editor = "Eckehard Sch{\"o}ll and Klapp, {Sabine H.} and Philipp H{\"o}vel",
booktitle = "Control of Self-Organising Nonlinear Systems",
address = "Germany",

}

D'Huys, O, Jüngling, T & Kinzel, W 2016, On the Interplay of Noise and Delay in Coupled Oscillators. in E Schöll, SH Klapp & P Hövel (eds), Control of Self-Organising Nonlinear Systems. Understanding Complex Systems Springer Complexity, Springer, pp. 127-145. https://doi.org/10.1007/978-3-319-28028-8_7

On the Interplay of Noise and Delay in Coupled Oscillators. / D'Huys, Otti; Jüngling, Thomas; Kinzel, Wolfgang.

Control of Self-Organising Nonlinear Systems. ed. / Eckehard Schöll; Sabine H. Klapp; Philipp Hövel. Springer, 2016. p. 127-145 (Understanding Complex Systems Springer Complexity).

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

TY - CHAP

T1 - On the Interplay of Noise and Delay in Coupled Oscillators

AU - D'Huys, Otti

AU - Jüngling, Thomas

AU - Kinzel, Wolfgang

PY - 2016

Y1 - 2016

N2 - Coupling delays can play an important role in the dynamics of various networks, such as coupled semiconductor lasers, communication networks, genetic transcription circuits or the brain. A well established effect of a delay is to induce multistability: In oscillatory systems a delay gives rise to coexistent periodic orbits with different frequencies and oscillation patterns. Adding noise to the dynamics, the network switches stochastically between these delay-induced orbits. For phase oscillators, we compute analytically the distribution of frequencies, the robustness to noise and their dependence on system parameters as the coupling strength and coupling delay.

AB - Coupling delays can play an important role in the dynamics of various networks, such as coupled semiconductor lasers, communication networks, genetic transcription circuits or the brain. A well established effect of a delay is to induce multistability: In oscillatory systems a delay gives rise to coexistent periodic orbits with different frequencies and oscillation patterns. Adding noise to the dynamics, the network switches stochastically between these delay-induced orbits. For phase oscillators, we compute analytically the distribution of frequencies, the robustness to noise and their dependence on system parameters as the coupling strength and coupling delay.

KW - Stochastic dynamic systems

KW - time delay

KW - coupled systems

UR - https://link.springer.com/chapter/10.1007/978-3-319-28028-8_7

U2 - 10.1007/978-3-319-28028-8_7

DO - 10.1007/978-3-319-28028-8_7

M3 - Chapter (peer-reviewed)

SN - 978-3-319-28028-8; 978-3-319-28027-1

T3 - Understanding Complex Systems Springer Complexity

SP - 127

EP - 145

BT - Control of Self-Organising Nonlinear Systems

A2 - Schöll, Eckehard

A2 - Klapp, Sabine H.

A2 - Hövel, Philipp

PB - Springer

ER -

D'Huys O, Jüngling T, Kinzel W. On the Interplay of Noise and Delay in Coupled Oscillators. In Schöll E, Klapp SH, Hövel P, editors, Control of Self-Organising Nonlinear Systems. Springer. 2016. p. 127-145. (Understanding Complex Systems Springer Complexity). https://doi.org/10.1007/978-3-319-28028-8_7