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

Abstract

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.

arXiv comment6 pages, 9 figures, accepted for publication in Phys. Rev. E

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Cited by in corpus (3)

• Self-organized criticality in single neuron excitability
• Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise
• Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation