Verechtchaguina, T., Sokolov, I. M., Schimansky-Geier, L. (March 2006) First passage time densities in resonate-and-fire models. Phys Rev E Stat Nonlin Soft Matter Phys, 73 (3 Pt 1). 031108. ISSN 1539-3755 (Print)1539-3755 (Linking)
Abstract
Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for non-Markovian differentiable random processes. We start from an exact expression for the FPT density in terms of an infinite series of integrals over joint densities of level crossings, and consider different approximations based on truncation or on approximate summation of this series. Thus the first few terms of the series give good approximations for the FPT density on short times. For rapidly decaying correlations the decoupling approximations perform well in the whole time domain. As an example we consider resonate-and-fire neurons representing stochastic underdamped or moderately damped harmonic oscillators driven by white Gaussian or by Ornstein-Uhlenbeck noise. We show that approximations reproduce all qualitatively different structures of the FPT densities: from monomodal to multimodal densities with decaying peaks. The approximations work for the systems of whatever dimension and are especially effective for the processes with narrow spectral density, exactly when Markovian approximations fail.
| Item Type: | Paper |
|---|---|
| Uncontrolled Keywords: | Action Potentials/*physiology Animals Biological Clocks/*physiology Cell Membrane/*physiology Computer Simulation Differential Threshold/physiology Excitatory Postsynaptic Potentials/*physiology Humans Membrane Potentials/physiology *Models, Neurological Models, Statistical Neurons/*physiology Stochastic Processes Synaptic Transmission/*physiology |
| Subjects: | organs, tissues, organelles, cell types and functions > tissues types and functions > membranes organs, tissues, organelles, cell types and functions > tissues types and functions > neural networks organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons organs, tissues, organelles, cell types and functions > cell types and functions > cell types > neurons |
| CSHL Authors: | |
| Communities: | CSHL labs > Engel lab |
| Depositing User: | Matt Covey |
| Date: | March 2006 |
| Date Deposited: | 14 Aug 2017 20:12 |
| Last Modified: | 14 Aug 2017 20:12 |
| Related URLs: | |
| URI: | https://repository.cshl.edu/id/eprint/35098 |
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