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Chaos / Volume 21 / Issue 4 / FOCUS ISSUE: NONLINEAR AND STOCHASTIC PHYSICS IN BIOLOGY

Chaos 21, 047515 (2011); http://dx.doi.org/10.1063/1.3665201 (10 pages)

Huygens (and others) revisited

Kurt Wiesenfeld and Daniel Borrero-Echeverry

Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA

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(Received 30 August 2011; accepted 11 November 2011; published online 29 December 2011)

We develop a generic iterative map model of coupled oscillators based on simple physical processes common to many such systems. The model allows us to understand, from a unified perspective, the range of different outcomes reported for experiments by Huygens and modern realizations of his two coupled clocks.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MAP DESCRIPTION
    1. Single element
    2. Coupled elements
  3. ANALYSIS OF THE MAP
    1. In-phase and antiphase fixed points
    2. Stability of the in-phase state
      1. Case I: complex conjugate eigenvalues
      2. Case II: real eigenvalues, μ > 0
      3. Case III: real eigenvalues, μ < 0
    3. Stability of the antiphase state
      1. Case I: complex conjugate eigenvalues
      2. Case II: real eigenvalues, μ > 0
      3. Case III: real eigenvalues, μ < 0
  4. PLATFORM-COUPLED CLOCKS AND METRONOMES
  5. DISCUSSION

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KEYWORDS and PACS

Keywords

large-scale systems, nonlinear dynamical systems, oscillators, synchronisation

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3665201

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    H. Ulrichs, A. Mann, and U. Parlitz, Chaos 19, 043120 (2009)CHAOEH000019000004043120000001.

    R. Dilão, Chaos 19, 023118 (2009)CHAOEH000019000002023118000001.

    K. Czolczynski, P. Perlikowski, A. Stefanski, and T. Kapitaniak, Chaos 21, 023129 (2011)CHAOEH000021000002023129000001.


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