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Quantifying the nonlinear complexity of optical time-delayed chaotic systems based on reservoir computing.

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Area of Science:

  • Nonlinear Dynamics
  • Optical Engineering
  • Complex Systems

Background:

  • Optical time-delayed (TD) chaotic systems are crucial for secure communications.
  • Quantifying their dynamical complexity is essential for performance and security analysis.
  • Existing complexity metrics like permutation entropy may not fully capture system dynamics.

Purpose of the Study:

  • To propose a novel method for measuring the dynamical complexity of optical TD chaotic systems.
  • To introduce a complexity metric based on reservoir computing (RC) network learning performance.
  • To compare the proposed metric with established indicators for optical chaotic time series.

Main Methods:

  • Utilized reservoir computing (RC) networks to learn the mapping between system output and its time-delayed variant.
  • Quantified the RC network's learning performance as a complexity metric.
  • Evaluated the metric's responsiveness against permutation entropy, fractal dimension, and maximal Lyapunov exponent using two optical TD chaotic generators.
  • Investigated the relationship between the complexity metric and the time-delay signature.

Main Results:

  • The proposed RC-based complexity metric effectively quantifies the difficulty of reconstructing system dynamics.
  • The new metric demonstrated higher responsiveness to parameter variations in optical TD chaotic systems compared to traditional methods.
  • An inverse relationship was observed between the complexity metric and the time-delay signature across a broad parameter range.

Conclusions:

  • The developed complexity metric offers a sensitive tool for analyzing optical TD chaotic systems.
  • This method provides a novel perspective for security evaluation of optical chaotic generators based on dynamics reconstruction.
  • The findings contribute to a deeper understanding of complexity-dynamics relationships in optical chaotic systems.