Jove
Visualize
Contact Us

Related Experiment Videos

Identification methods for nonlinear stochastic systems.

Jose-Maria Fullana1, Maurice Rossi

  • 1Laboratoire de Modélisation en Mécanique UMR 7607, Université Paris VI, 4 Place Jussieu, 75005 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
Summary

This study extends orbit tracking for model identification to stochastic differential equations. It introduces a novel method using ensemble averages and variances to determine system parameters from time series data.

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

Behaviour of silica nanoparticles in dermis-like cellularized collagen hydrogels.

Biomaterials science·2020
Same author

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals.

Journal of biomechanical engineering·2016
Same author

Fluid friction and wall viscosity of the 1D blood flow model.

Journal of biomechanics·2016
Same author

Chemical convection in the methylene-blue-glucose system: Optimal perturbations and three-dimensional simulations.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014
Same author

Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.

Computer methods in biomechanics and biomedical engineering·2014
Same author

Collective dynamics in coupled maps on a lattice with quenched disorder.

Physical review. E, Statistical, nonlinear, and soft matter physics·2006
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:

  • Dynamical Systems and Control Theory
  • Computational Physics
  • Statistical Mechanics

Background:

  • Traditional orbit tracking methods are limited in identifying complex systems.
  • Stochastic differential equations (SDEs) are crucial for modeling systems with inherent randomness.
  • Accurate parameter estimation is vital for understanding and predicting the behavior of dynamical systems.

Purpose of the Study:

  • To extend model identification techniques based on orbit tracking to stochastic differential equations.
  • To develop a method for parameter estimation in SDEs using deterministic and statistical features.
  • To validate the proposed method on a well-known chaotic system, the Lorenz system.

Main Methods:

  • Introducing deterministic and statistical features through the time evolution of ensemble averages and variances.

Related Experiment Videos

  • Deriving deterministic equations for these quantities under linear and weakly nonlinear approximations.
  • Defining a cost function based on the derived equations and observed time series data.
  • Employing simulated annealing and backpropagation algorithms for cost function minimization to find best-fit parameters.

    • Main Results:

    • Deterministic equations governing ensemble averages and variances were explicitly derived.
    • The developed parameter estimation procedure was successfully applied to a stochastic Lorenz system.
    • The method demonstrated effectiveness across various sampling time intervals.

    Conclusions:

    • The proposed approach effectively extends orbit tracking for model identification to stochastic differential equations.
    • The method provides a robust framework for parameter estimation in complex, noisy dynamical systems.
    • This work offers a valuable tool for analyzing and understanding systems described by SDEs.