Populations of Attractor Cycle Oscillators

  • Arthur T. Winfree
Part of the Biomathematics book series (SSE)


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 attractor 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 attractor cycle oscillators considered in this chapter.


Area Element Attractor Cycle Phase Singularity Chemical Oscillator Stimulus Magnitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Biological Sciences, Lilly Hall of Life SciencesPurdue UniversityWest LafayetteUSA

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