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Reliability of Coupled Oscillators

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, Tucson, AZ, USA

    Kevin K. Lin

  2. Department of Applied Mathematics, University of Washington, Seattle, WA, USA

    Eric Shea-Brown

  3. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Lai-Sang Young

Authors
  1. Kevin K. Lin
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  2. Eric Shea-Brown
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  3. Lai-Sang Young
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Correspondence to Kevin K. Lin.

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Lin, K.K., Shea-Brown, E. & Young, LS. Reliability of Coupled Oscillators. J Nonlinear Sci 19, 497–545 (2009). https://doi.org/10.1007/s00332-009-9042-5

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  • DOI: https://doi.org/10.1007/s00332-009-9042-5

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