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Updated: May 22, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Random dynamical models from time series
Y I Molkov1, E M Loskutov, D N Mukhin
1Indiana University - Purdue University, Indianapolis, Indiana, USA. ymolkov@iupui.edu
Summary
This study introduces a Bayesian method using artificial neural networks to model random dynamical systems from time series data. The approach accurately reproduces system behavior and predicts future changes, demonstrating its effectiveness on complex noise models.
Area of Science:
- Dynamical Systems
- Machine Learning
- Bayesian Inference
Background:
- Stochastic dynamical systems are prevalent in various scientific fields.
- Modeling these systems often involves complex time series data.
- Traditional methods may struggle with non-Gaussian noise and non-autonomous behavior.
Purpose of the Study:
- To develop a consistent Bayesian framework for modeling stochastic dynamical systems using time series.
- To implement this framework using artificial neural networks.
- To demonstrate the model's capability in reproducing stationary behavior and predicting qualitative changes.
Main Methods:
- Formulation of a Bayesian approach for stochastic dynamical systems.
- Implementation via artificial neural networks.
- Validation on model examples including discrete maps and flow systems with Langevin force.
Main Results:
- The proposed Bayesian method successfully models stochastic dynamical systems.
- The approach accurately reproduces observed stationary regimes.
- The method demonstrates predictive power for qualitative behavioral changes in weakly non-autonomous systems.
Conclusions:
- The Bayesian approach with artificial neural networks provides a robust method for modeling stochastic dynamical systems.
- This technique is effective for both reproducing current behavior and predicting future dynamics.
- The approach is validated on diverse systems with complex noise characteristics.
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