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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Published on: December 9, 2015

Stochastic modelling of intermittency.

Thomas Stemler1, Johannes P Werner, Hartmut Benner

  • 1School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley 6009, WA, Australia. thomas@maths.uwa.edu.au

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 2, 2009
PubMed
Summary
This summary is machine-generated.

This study models chaotic systems using stochastic differential equations, finding that crisis-induced intermittency is accurately captured by state-space-dependent diffusion in electronic circuits.

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Stochastic Processes and Modeling
  • Experimental Physics and Engineering

Background:

  • Stochastic differential equations (SDEs) are increasingly used to model low-dimensional chaotic systems.
  • Accurate modeling often relies on assumptions like time-scale separation, which may not hold in real-world chaotic dynamics.
  • Understanding the applicability and limitations of SDEs for chaotic systems is crucial for reliable data analysis.

Purpose of the Study:

  • To test the efficacy of SDE-based modeling for chaotic systems in an experimental setting.
  • To determine drift and diffusion coefficients without assuming pronounced time-scale separation.
  • To establish criteria for the successful application of stochastic models to chaotic time series.

Main Methods:

  • Implementation of stochastic differential equation models for an electronic circuit exhibiting chaotic behavior.
  • Experimental data acquisition from the chaotic electronic circuit.
  • Comparison of analytical solutions of the Fokker-Planck equation with experimental data.
  • Numerical simulations to explore the limits of the stochastic modeling approaches.

Main Results:

  • Crisis-induced intermittency in the chaotic electronic circuit can be effectively described by a stochastic model.
  • The model's success is attributed to state-space-dependent diffusion, even without clear time-scale separation.
  • Numerical simulations identified specific limitations of the stochastic modeling techniques.

Conclusions:

  • Stochastic differential equations, particularly those with state-space-dependent diffusion, provide a viable framework for modeling crisis-induced intermittency in chaotic systems.
  • The study successfully obtained reliable model parameters from experimental data without strict time-scale separation assumptions.
  • A criterion was established to assess the suitability of stochastic models for capturing essential features of chaotic time series.