Getting off the Ring

  • Arthur T. Winfree
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 12)


My purpose in this chapter is to start “putting flesh on the bones” of the simple clock metaphor. Up to this point, I’ve tried to hold your attention on “phase” and its rate of change by confining discussion to the simplest metaphor of smooth cyclic dynamics, namely, the ring device. I have studiously avoided allusion to other degrees of freedom of the “state” of any biological clock. To make the transition to a broader perspective in an orderly way, I now wish to introduce just one additional notion, i.e., that a rhythmic --process might be adjustable not only in phase, our exclusive preoccupation in previous chapters, but also in some measure of its vigor, amplitude, range, or degree of variation during the cycle.


State Space Stimulus Duration Medium Height Phase Singularity Stimulus Magnitude 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of ArizonaTucsonUSA

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