Abstract
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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Bibliography
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.
G. B. Ermentrout, Type I membranes, phase resetting curves, and synchrony, Neural Comp., 8 (1996), pp. 879–1001.
A. L. Hodgkin, The local changes associated with repetitive action in a non-medullated axon, J. Physiol. (London), 107 (1948), pp. 165–181.
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.
S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2nd ed., 2015.
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Börgers, C. (2017). Model Neurons of Bifurcation Type 1. In: An Introduction to Modeling Neuronal Dynamics. Texts in Applied Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-51171-9_12
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DOI: https://doi.org/10.1007/978-3-319-51171-9_12
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