The Variety of Channels

  • G. Bard ErmentroutEmail author
  • David H. Terman
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 35)


We have discussed several types of active (voltage-gated) channels for specific neuron models. The Hodgkin–Huxley model for the squid axon consisted of three different ion channels: a passive leak, a transient sodium channel, and the delayed rectifier potassium channel. Similarly, the Morris–Lecar model has a delayed rectifier and a simple calcium channel (with no dynamics). Hodgkin and Huxley were smart and supremely lucky that they used the squid axon as a model to analyze the action potential, as it turns out that most neurons have dozens of different ion channels. In this chapter, we briefly describe a number of them, provide some instances of their formulas, and describe how they influence a cell’s firing properties. The reader who is interested in finding out about other channels and other models for the channels described here should consult, which is a database for neural models.


Firing Rate Hopf Bifurcation Sodium Current Fold Point Squid Axon 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Dept. MathematicsOhio State UniversityColumbusUSA

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