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Basin stability for updating system uncertainties.

Dawid Dudkowski1, Tomasz Kapitaniak1

  • 1Division of Dynamics, <a href="https://ror.org/00s8fpf52">Lodz University of Technology</a>, Stefanowskiego 1/15, 90-537 Lodz, Poland.

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Summary
This summary is machine-generated.

This study introduces a basin stability tool to update system properties under uncertainty. It uses Bayesian inference on coupled pendula to probabilistically refine knowledge of complex dynamical systems.

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Area of Science:

  • Physics
  • Dynamical Systems Theory
  • Complex Systems

Background:

  • Complex dynamical systems often exhibit multiple coexisting behaviors (attractors).
  • Parameter uncertainties in these systems complicate the analysis of their stability and behavior.
  • Basin stability analysis quantifies the robustness of different system behaviors.

Purpose of the Study:

  • To develop and apply a basin stability framework for updating system property knowledge under parameter uncertainty.
  • To integrate basin stability mapping with Bayesian inference for probabilistic characterization of complex systems.
  • To investigate the impact of parameter variations on basin stability calculations, especially near existence borders.

Main Methods:

  • Utilized a classical mechanical model of coupled pendula exchanging energy through a supporting structure.
  • Calculated basin stability maps for distinct dynamical behaviors (synchronous patterns, desynchronization).
  • Employed Bayesian inference to combine prior parameter distributions with attractor occurrence data.

Main Results:

  • Demonstrated how basin stability maps, when combined with Bayesian inference, yield updated posterior probability distributions for system properties.
  • Showcased that attractor occurrence data refines knowledge of system parameters probabilistically.
  • Highlighted significant differences in basin stability estimation when parameter variations are considered versus fixed parameters, particularly near behavior existence borders.

Conclusions:

  • The proposed application of basin stability analysis offers a probabilistic approach to studying complex dynamical systems.
  • This method enhances understanding of system properties by updating information under parameter uncertainties.
  • Careful consideration of estimation methods, especially near existence borders, is crucial for reliable applications.