Nonequilibrium dynamics of stochastic point processes with refractoriness

Moritz Deger, Moritz Helias, Stefano Cardanobile, Fatihcan M. Atay, and Stefan Rotter
Phys. Rev. E 82, 021129 – Published 31 August 2010

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 nonstationary renewal processes.

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  • Received 22 February 2010
  • Publisher error corrected 8 September 2010

DOI:https://doi.org/10.1103/PhysRevE.82.021129

©2010 American Physical Society

Corrections

8 September 2010

Erratum

Publisher's Note: Nonequilibrium dynamics of stochastic point processes with refractoriness [Phys. Rev. E 82, 021129 (2010)]

Moritz Deger, Moritz Helias, Stefano Cardanobile, Fatihcan M. Atay, and Stefan Rotter
Phys. Rev. E 82, 039902 (2010)

Authors & Affiliations

Moritz Deger1,*, Moritz Helias2,†, Stefano Cardanobile1, Fatihcan M. Atay3, and Stefan Rotter1

  • 1Bernstein Center Freiburg and Faculty of Biology, Albert-Ludwig University, 79104 Freiburg, Germany
  • 2RIKEN Brain Science Institute, Wako City, Saitama 351-0198, Japan
  • 3Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

  • *Corresponding author; deger@bcf.uni-freiburg.de
  • Corresponding author; helias@brain.riken.jp

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Issue

Vol. 82, Iss. 2 — August 2010

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