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

Miguel Angel Durán Roa·Mauro Copelli·Osame Kinouchi·Nestor Caticha
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Abstract

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $τ$ near but below the repetitive firing critical current, $τ\simeq C (I_c-I)^{-Δ}$. 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 $Δ= 1/2$. 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.

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Miguel Angel Durán Roa, Mauro Copelli, Osame Kinouchi, Nestor Caticha. 2007-01-24. Scaling law for the transient behavior of type-II neuron models. https://doi.org/10.1103/physreve.75.021911

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