Jove
Visualize
Contact Us

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.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

BacilliFinder: Revolutionizing Tuberculosis Detection with Computer Vision.

The Indian journal of tuberculosis·2025
Same author

Miniature inverted-repeat transposable elements (MITEs), derived insertional polymorphism as a tool of marker systems for molecular plant breeding.

Molecular biology reports·2020
Same author

Wound healing activity of <i>Delonix elata</i> stem bark extract and its isolated constituent quercetin-3-rhamnopyranosyl-(1-6) glucopyranoside in rats.

Journal of pharmaceutical analysis·2018
Same author

Antioxidant and prophylactic effects of Delonix elata L., stem bark extracts, and flavonoid isolated quercetin against carbon tetrachloride-induced hepatotoxicity in rats.

BioMed research international·2014
Same author

Direct and indirect method of plant regeneration from root explants of Caesalpinia bonduc (L.) Roxb.--a threatened medicinal plant of Western Ghats.

Indian journal of experimental biology·2013
Same author

Biochemical markers assisted screening of Fusarium wilt resistant Musa paradisiaca (L.) cv. puttabale micropropagated clones.

Indian journal of experimental biology·2013
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

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.

Related Experiment Videos

  • 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.