title: Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays.
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.
authors.affiliation: Institute for Theoretical Physics, University of Münster, Germany.
authors.forename: T D
authors.initials: TD
authors.lastname: Frank