Reliability of coupled oscillators

Kevin Lin, Eric Shea-Brown, Lai Sang Young

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. Single oscillators are well known to be reliable. We show in this paper that unreliable behavior can occur in a network as small as a coupled oscillator pair in which the signal is received by the first oscillator and relayed to the second with feedback. A geometric explanation based on shear-induced chaos at the onset of phase-locking is proposed. We treat larger networks as decomposed into modules connected by acyclic graphs, and give a mathematical analysis of the acyclic parts. Moreover, for networks in this class, we show how the source of unreliability can be localized, and address questions concerning downstream propagation of unreliability once it is produced.

Original languageEnglish (US)
Pages (from-to)497-545
Number of pages49
JournalJournal of Nonlinear Science
Volume19
Issue number5
DOIs
StatePublished - Oct 2009

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Coupled Oscillators
Chaos theory
Feedback
Phase Locking
Mathematical Analysis
Chaos
Initial conditions
Propagation
Module
Graph in graph theory

Keywords

  • Coupled oscillators
  • Neural network dynamics
  • Random dynamical systems

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Engineering(all)

Cite this

Reliability of coupled oscillators. / Lin, Kevin; Shea-Brown, Eric; Young, Lai Sang.

In: Journal of Nonlinear Science, Vol. 19, No. 5, 10.2009, p. 497-545.

Research output: Contribution to journalArticle

Lin, Kevin ; Shea-Brown, Eric ; Young, Lai Sang. / Reliability of coupled oscillators. In: Journal of Nonlinear Science. 2009 ; Vol. 19, No. 5. pp. 497-545.
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