Wave Propagation in Excitable Systems

  • James Keener
  • James Sneyd
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 8/1)

The problem of current flow in the axon of a nerve is much more complicated than that of flow in dendritic networks (Chapter 4). Recall from Chapter 5 that the voltage dependence of the ionic currents can lead to excitability and action potentials. In this chapter we show that when an excitable membrane is incorporated into a nonlinear cable equation, it can give rise to traveling waves of electrical excitation. Indeed, this property is one of the reasons that the Hodgkin—Huxley equations are so important. In addition to producing a realistic description of a space-clamped action potential, Hodgkin and Huxley showed that this action potential propagates along an axon with a fixed speed, which could be calculated.

However, the nerve axon is but one of many examples of a spatially extended excitable system in which there is propagated activity. For example, propagated waves of electrical or chemical activity are known to occur in skeletal and cardiac tissue, in the retina, in the cortex of the brain, and within single cells of a wide variety of types. In this chapter we describe this wave activity, beginning with a discussion of propagated electrical activity along one-dimensional cables, then concluding with a brief discussion of waves in higher-dimensional excitable systems.


Wave Front Dispersion Curve Travel Wave Solution Excitable Medium Spiral Wave 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • James Keener
    • 1
  • James Sneyd
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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