dorsal/arxiv
View SchemaFirst Passage Time Densities in Resonate-and-Fire Models
| Authors | T. Verechtchaguina, I. M. Sokolov, L. Schimansky-Geier |
|---|---|
| Categories | |
| ArXiv ID | physics/0512081 |
| URL | https://arxiv.org/abs/physics/0512081 |
| DOI | 10.1103/PhysRevE.73.031108 |
Abstract
Motivated by the dynamics of resonant neurons we discuss the properties of the first passage time (FPT) densities for nonmarkovian 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.
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"abstract": "Motivated by the dynamics of resonant neurons we discuss the properties of\nthe first passage time (FPT) densities for nonmarkovian differentiable random\nprocesses. We start from an exact expression for the FPT density in terms of an\ninfinite series of integrals over joint densities of level crossings, and\nconsider different approximations based on truncation or on approximate\nsummation of this series. Thus, the first few terms of the series give good\napproximations for the FPT density on short times. For rapidly decaying\ncorrelations the decoupling approximations perform well in the whole time\ndomain.\n As an example we consider resonate-and-fire neurons representing stochastic\nunderdamped or moderately damped harmonic oscillators driven by white Gaussian\nor by Ornstein-Uhlenbeck noise. We show, that approximations reproduce all\nqualitatively different structures of the FPT densities: from monomodal to\nmultimodal densities with decaying peaks. The approximations work for the\nsystems of whatever dimension and are especially effective for the processes\nwith narrow spectral density, exactly when markovian approximations fail.",
"arxiv_id": "physics/0512081",
"authors": [
"T. Verechtchaguina",
"I. M. Sokolov",
"L. Schimansky-Geier"
],
"categories": [
"physics.data-an",
"physics.bio-ph"
],
"doi": "10.1103/PhysRevE.73.031108",
"title": "First Passage Time Densities in Resonate-and-Fire Models",
"url": "https://arxiv.org/abs/physics/0512081"
},
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