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

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

2006-06-14

arxiv.org/abs/q-bio/0606019v2

Phys. Rev. E 75, 021911 (2007)

Biology

Quantitative Biology

Neurons and Cognition

6 pages, 9 figures, accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.75.021911

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.

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