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Accurately determining limit cycle position in phase space is crucial for data-driven modeling of oscillatory systems. This study introduces a method using Sparse Identification of Nonlinear Dynamics (SINDy) to improve model accuracy by analyzing offset datasets.

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Area of Science:

  • * Dynamical systems and differential equations
  • * Computational and data-driven modeling
  • * Nonlinear dynamics and chaos theory

Background:

  • * Oscillatory behavior is common in dynamical systems and often modeled using differential equations.
  • * Data-driven methods, like Sparse Identification of Nonlinear Dynamics (SINDy), are increasingly used to derive these models.
  • * Accurate identification of a system's limit cycle position in phase space is vital for effective model discovery.

Purpose of the Study:

  • * To highlight the significance of precise limit cycle positioning for sparse and effective dynamical system models.
  • * To introduce a novel method for identifying limit cycle positions and nullclines using SINDy on offset datasets.
  • * To evaluate the proposed method's performance based on model complexity, coefficient of determination, and generalization error.

Main Methods:

  • * Application of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm.
  • * Systematic adjustment of datasets with various offsets to probe limit cycle behavior.
  • * Evaluation of identified models using criteria including complexity, R-squared, and generalization error.

Main Results:

  • * The method successfully identified limit cycle positions and nullclines across diverse oscillatory models.
  • * Incorporating detailed limit cycle information demonstrably improved the accuracy of identified dynamical system models.
  • * Tested models include the FitzHugh-Nagumo model, coupled cubic equations, and glycolytic oscillations.

Conclusions:

  • * Accurate determination of limit cycle position in phase space is essential for robust data-driven modeling of oscillatory systems.
  • * The proposed SINDy-based approach effectively enhances the accuracy of identified models by leveraging limit cycle information.
  • * This method offers a valuable tool for understanding and modeling complex oscillatory phenomena.