Journal of Nonlinear Science

, Volume 19, Issue 5, pp 497–545 | Cite as

Reliability of Coupled Oscillators

  • Kevin K. LinEmail author
  • Eric Shea-Brown
  • Lai-Sang Young


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.


Coupled oscillators Random dynamical systems Neural network dynamics 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Kevin K. Lin
    • 1
    Email author
  • Eric Shea-Brown
    • 2
  • Lai-Sang Young
    • 3
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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