Issue |
Europhys. Lett.
Volume 65, Number 3, February 2004
|
|
---|---|---|
Page(s) | 434 - 439 | |
Section | Interdisciplinary physics and related areas of science and technology | |
DOI | https://doi.org/10.1209/epl/i2003-10091-5 | |
Published online | 01 January 2004 |
Application of a generalised Levy residence time problem to neuronal dynamics
1
Centre for the Study of Evolution, University of Sussex Brighton BN1 9QG, Sussex, UK
2
Department of Informatics, University of Sussex Brighton BN1 9QG, Sussex, UK
Corresponding author: D.Waxman@sussex.ac.uk
Received:
22
September
2003
Accepted:
21
November
2003
The distribution of bursting lengths of neuron spikes, in a
two-component integrate-and-fire model, is investigated. The
stochastic process underlying this model corresponds to a
generalisation of the Brownian motion underlying Levy's arcsine
law of residence times. The generalisation involves the inclusion
of a quadratic potential of strength γ and
corresponds to Levy's original problem. In the generalised
problem, the distribution of the residence times, T, over a
time window t, is related to spectral properties of a complex,
non-relativistic Hamiltonian of quantum mechanics. The
distribution of T depends on
and varies from a
U-shaped distribution for small
to a bell-shaped
distribution for large
. The first two moments of T
of the generalised problem are explicitly calculated and the
crossover point between the two forms of the distribution is
calculated. The distribution of residence times is shown to be
independent of the magnitude of the stochastic force. This
corresponds, in the neuron model, to exactly balanced synaptic
inputs and, in this case, the distribution of residence times
contains no information on synaptic inputs.
PACS: 87.19.La – Neuroscience / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 87.18.Sn – Neural networks
© EDP Sciences, 2004
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