Populations of Attracting-Cycle Oscillators

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


Chapter 4 provides a preliminary look at the phenomena to which we now turn: the phenomena typical of aggregates of oscillators. Just as the oscillator populations of physics comprise a very special case with very special properties (associated with linearity, energy conservation, etc.), so did the simple clocks of Chapter 4 comprise another very special case with very special properties (associated with the one-dimensionality of their state space). My objective in this chapter is to organize under the same four headings as in Chapter 4 some discussions and examples of what I take to be the characteristic behavior of attracting-cycle oscillators in populations and communities. Such oscillators can have any number (≥2) of variables mutually determining their rates of change in nonlinear ways. Linear oscillators, conservative oscillators, and simple clocks are special limiting cases of the attracting-cycle oscillators considered in this chapter.


State Space Concentric Ring Area Element Phase Singularity Stimulus Magnitude 
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  1. 1.
    Their excellent paper in Science was delayed in publication by the referee’s (my) insistence on that experiment; meanwhile Thoene’s (1973) almost identical paper appeared in Nature, but without the critical experiment. The same experiment, in this case proving that electrical wave trains in the brain are not pseudowaves, was performed by Petsche et al. (1970) and Petsche and Rappelsberger (1970).Google Scholar

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© 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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