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Related Experiment Videos

Damped stochastic system driven by colored noise: analytical solution by a path integral approach

Mahanta1, Venkatesh

  • 1Department of Electrical Engineering, Indian Institute of Technology, Delhi Hauz Khas, New Delhi 110 016, India.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

This study analyzes a nonlinear dynamical system with Ornstein-Uhlenbeck noise. We derived an approximate Fokker-Planck equation and computed the stationary probability density function, validating it with simulations.

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Area of Science:

  • Nonlinear dynamics
  • Stochastic processes
  • Statistical physics

Background:

  • Damped nonlinear dynamical systems are fundamental in various scientific fields.
  • Understanding systems driven by non-Markovian noise, like Ornstein-Uhlenbeck, is crucial.
  • Stochastic processes introduce randomness that requires advanced analytical methods.

Purpose of the Study:

  • To investigate a nonlinear non-Markovian stochastic process.
  • To derive an approximate Fokker-Planck-type equation for the system.
  • To compute and validate the stationary probability density function (SPDF).

Main Methods:

  • Utilized the path-integral approach to derive the Fokker-Planck equation.
  • Employed the matrix continued fraction method for SPDF computation.

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  • Performed digital simulations for result validation.

    • Main Results:

    • Successfully derived an approximate Fokker-Planck-type equation.
    • Computed the SPDF for the nonlinear stochastic process.
    • Demonstrated favorable agreement between computed and simulated SPDFs.

    Conclusions:

    • The path-integral and matrix continued fraction methods are effective for analyzing such systems.
    • The derived SPDF accurately represents the system's long-term behavior.
    • This work provides a robust framework for studying nonlinear stochastic systems.