Stochastic Biomathematical Models by Mostafa Bachar Jerry Batzel & Susanne Ditlevsen

Author:Mostafa Bachar, Jerry Batzel & Susanne Ditlevsen
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5.14)

Despite the excellent fitting with some experimental data, the Gerstein and Mandelbrot model was criticized for its biological simplifications [134]. However, it allows one to obtain results that help the intuition for more realistic models and it is still used for this purpose, taking advantage of the existence of a closed form FPT pdf through a constant boundary.

Its FPT pdf is known also through particular time dependent boundaries. These FPTs can be used to account for the refractory period following a spike. Indeed, a time varying boundary, assuming high values at small times and then decreasing, makes short ISIs rare. The FPT pdf is known for a continuous piecewise-linear boundary , where and , with . If , such boundary is linear and the FPT pdf is

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