Scaling law for the transient behavior of type-II neuron models

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times \(\tau\) near but below the repetitive firing critical current, \(\tau \simeq C (I_c-I)^{-\Delta}\). For both the Hodgkin-Huxley and Morris-Lecar models we find that the critical...

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Bibliographic Details
Published in:arXiv.org 2007-01
Main Authors: Durán Roa, Miguel Angel, Copelli, Mauro, Kinouchi, Osame, Caticha, Nestor
Format: Article
Language:English
Subjects:
Critical current (superconductivity)
Mathematical models
Numerical integration
Scaling laws
Online Access:Get full text
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Summary:We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times \(\tau\) near but below the repetitive firing critical current, \(\tau \simeq C (I_c-I)^{-\Delta}\). For both the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent is independent of the numerical integration time step and that both systems belong to the same universality class, with \(\Delta = 1/2\). For appropriately chosen parameters, the FitzHugh-Nagumo model presents the same generic transient behavior, but the critical region is significantly smaller. We propose an experiment that may reveal nontrivial critical exponents in the squid axon.
ISSN:2331-8422
DOI:10.48550/arxiv.0606019