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Related Experiment Video

Updated: Jul 7, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Monte Carlo method for multiparameter estimation in coupled chaotic systems.

Inés P Mariño1, Joaquín Míguez

  • 1Departamento de Física, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain. ines.perez@urjc.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
Summary

We developed a Monte Carlo optimization method to estimate parameters in chaotic dynamical models using time series data. This approach synchronizes model and data to minimize errors, successfully applied to the Lorenz system.

Related Experiment Videos

Last Updated: Jul 7, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Computational Physics
  • Time Series Analysis

Background:

  • Estimating parameters in chaotic dynamical models from scalar time series is challenging.
  • Chaotic systems exhibit sensitive dependence on initial conditions, complicating parameter inference.
  • Synchronization between a model and observed data offers a potential pathway for parameter estimation.

Purpose of the Study:

  • To propose an efficient Monte Carlo optimization algorithm for estimating multiple parameters of chaotic dynamical models.
  • To enable accurate parameter estimation by minimizing synchronization error between a model and observed time series.
  • To demonstrate the algorithm's efficacy on a canonical chaotic system, the Lorenz system.

Main Methods:

  • A Monte Carlo optimization algorithm is proposed to iteratively update model parameters.
  • The algorithm minimizes the synchronization error between the chaotic model and the observed scalar time series.
  • Synchronization is achieved by adjusting the coupling between the model and the data-generating system.

Main Results:

  • The proposed algorithm efficiently estimates multiple parameters of chaotic dynamical models.
  • Joint estimation of three static parameters for the chaotic Lorenz system was successfully performed.
  • The method effectively minimizes synchronization error, indicating accurate parameter recovery.

Conclusions:

  • The developed Monte Carlo optimization algorithm provides an efficient solution for parameter estimation in chaotic systems.
  • The synchronization-based approach is effective for inferring model parameters from scalar time series.
  • This method holds promise for applications in various fields relying on chaotic modeling.