Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays

T. D. Frank
Phys. Rev. E 71, 031106 – Published 21 March 2005

Abstract

We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L’Heureux, and Longtin. We derive an analytical expression for stationary distributions using first-order perturbation theory. We demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data. In addition, we show that the Fokker-Planck perspective for stochastic systems with time delays is consistent with the so-called extended phase-space approach to time-delayed systems.

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  • Received 7 October 2004

DOI:https://doi.org/10.1103/PhysRevE.71.031106

©2005 American Physical Society

Authors & Affiliations

T. D. Frank

  • Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany

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Vol. 71, Iss. 3 — March 2005

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