4.7 Article

Fokker-Planck perspective on stochastic delay systems: Exact solutions and data analysis of biological systems

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PHYSICAL REVIEW E
卷 68, 期 2, 页码 -

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AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.68.021912

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Stochastic delay systems with additive noise are examined from the perspective of Fokker-Planck equations. For a linear system, the exact stationary probability density is derived by means of a delay Fokker-Planck equation. We show how to determine the delay equation of the linear system from experimental data, and corroborate a fundamental result previously obtained by Kuchler and Mensch. We also propose a method to derive delay equations of nonlinear systems from experimental data. To this end, the theory of multivariate Fokker-Planck equations is used. The applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans.

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