Summary
A model for the generation of action potentials by a neuron is presented. This model is based on standard and commonly accepted properties of excitable cells (neurons). The novelty is that under quite natural assumptions the generation of action potentials is described as a special case of a general model for systems generating recurrent biological events. A formula for a density function of the membrane potential distribution in the firing times of the neuron is derived. An analysis of time intervals between spikes is of special interest. Three different interspike interval distributions are found, where one of them is close to the stable distribution. It is consistent with the well-known hypothesis that stable interspike intervals form part of the neural chain in which information is being preserved.
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Tyrcha, J. (2008). Dynamics of Integrate-and-Fire Models. In: Deutsch, A., et al. Mathematical Modeling of Biological Systems, Volume II. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4556-4_20
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DOI: https://doi.org/10.1007/978-0-8176-4556-4_20
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