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

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021912. doi: 10.1103/PhysRevE.68.021912. Epub 2003 Aug 22.

Abstract

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 Küchler 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.

MeSH terms

  • Biophysical Phenomena
  • Biophysics
  • Humans
  • Models, Statistical
  • Models, Theoretical
  • Movement*
  • Multivariate Analysis
  • Statistics as Topic
  • Stochastic Processes*