Excitable Kinetics and Excitable Media

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


Chapter 3 on ring devices is followed by Chapter 4 on populations and communities of such single-variable units: both simple clocks and the nonoscillating hourglasses. Chapter 6 on oscillators with more than one variable of state is followed by populations and communities in Chapter 8. What about nonoscillatory kinetics with more than one local state variable? That case is taken up here, together with consequences of interaction in spatially distributed communities. The upshot is a new kind of oscillator and a new kind of phase singularity, both of which are apparently exhibited in diverse chemical and physiological systems. Even though no isolated piece of it may oscillate, an excitable medium can organize itself spatially in a way that stabilizes oscillation at a characteristic period. Architecturally, this configuration more resembles a clock than anything encountered in previous chapters: It consists of crossed concentration gradients, any one of which might be taken as the clock’s “hand,” a pointer that physically rotates about a fixed pivot once in each cycle of oscillation. At the pivot, nothing changes; the pivot is a phase singularity and all the rest is built around it.


Vortex Ring Excitable Medium Spiral Wave Phase Singularity Fairy Ring 
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  1. 2.
    The eikonal equation formalizes the notion that every piece of wavefront advances parallel to itself at constant speed. See Keller (1958).Google Scholar

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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