

Preprint 53/2010
Nonequilibrium dynamics of stochastic point processes with refractoriness
Moritz Deger, Moritz Helias, Stefano Cardanobile, Fatihcan M. Atay, and Stefan Rotter
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Submission date: 22. Sep. 2010
Pages: 20
published in: Physical review / E, 82 (2010) 2, art-no. 021129
DOI number (of the published article): 10.1103/PhysRevE.82.021129
Bibtex
PACS-Numbers: 02.50.Ey, 87.19.ll, 87.18.Sn, 29.40.-n
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Abstract:
Stochastic point processes with refractoriness appear frequently in
the quantitative analysis of physical and biological systems, such
as the generation of action potentials by nerve cells, the release
and reuptake of vesicles at a synapse, and the counting of particles
by detector devices. Here we present an extension of renewal theory
to describe ensembles of point processes with time varying input.
This is made possible by a representation in terms of occupation numbers
of two states: Active and refractory. The dynamics of these occupation
numbers follows a distributed delay differential equation. In particular,
our theory enables us to uncover the effect of refractoriness on the
time-dependent rate of an ensemble of encoding point processes in
response to modulation of the input. We present exact solutions that
demonstrate generic features, such as stochastic transients and oscillations
in the step response as well as resonances, phase jumps and frequency
doubling in the transfer of periodic signals. We show that a large
class of renewal processes can indeed be regarded as special cases
of the model we analyze. Hence our approach represents a widely applicable
framework to define and analyze non-stationary renewal processes.