Model Neurons of Bifurcation Type 1

  • Christoph Börgers
Part of the Texts in Applied Mathematics book series (TAM, volume 66)


For a model neuron, there is typically a critical value I c with the property that for I < I c , there is a stable equilibrium with a low membrane potential, whereas periodic firing is the only stable behavior for I > I c , as long as I is not too high.

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  1. [9]
    D. Bianchi, A. Marasco, A. Limongiello, C. Marchetti, H. Marie, B. Tirozzi, and M. Migliore, On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons, J. Comp. Neurosci., 33 (2012), pp. 207–225.Google Scholar
  2. [47]
    G. B. Ermentrout, Type I membranes, phase resetting curves, and synchrony, Neural Comp., 8 (1996), pp. 879–1001.Google Scholar
  3. [75]
    A. L. Hodgkin, The local changes associated with repetitive action in a non-medullated axon, J. Physiol. (London), 107 (1948), pp. 165–181.Google Scholar
  4. [129]
    J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, in Methods in Neuronal Modeling, C. Koch and I. Segev, eds., Cambridge, MA, 1998, MIT Press, pp. 251–292.Google Scholar
  5. [149]
    S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2nd ed., 2015.Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Christoph Börgers
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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