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Area of Science:

  • Nonlinear Dynamics
  • Machine Learning
  • Chaos Theory

Background:

  • Inferring control parameters in nonlinear dynamical systems is crucial for understanding their behavior, especially with deterministic chaos.
  • Traditional methods often require system-specific models and complex parameterizations, limiting their broad application.

Purpose of the Study:

  • To develop and validate a novel methodology for inferring control parameters in nonlinear dynamical systems.
  • To demonstrate the effectiveness of using recurrence plots and convolutional neural networks for this task.

Main Methods:

  • Recurrence plots were used to represent nonlinear trajectories.
  • Convolutional neural networks were trained on these recurrence plots to infer control parameters.
  • The methodology was tested on the logistic map and the standard map.

Main Results:

  • The proposed approach accurately estimated control parameters for the tested nonlinear systems.
  • Recurrence plot-based methods showed significantly more robust results compared to direct time-series regression models.
  • Accurate parameter inference, combined with initial conditions, allows for deterministic system reconstruction.

Conclusions:

  • Recurrence-based learning frameworks offer a powerful tool for automated identification and characterization of nonlinear dynamical systems.
  • This methodology provides a generalizable and robust approach to parameter inference in nonlinear dynamics.
  • The findings advance the understanding and analysis of complex systems exhibiting chaotic behavior.