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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems.

Shaobo He1, Chunbiao Li2,3, Kehui Sun1

  • 1School of Physics and Electronics, Central South University, Changsha 410083, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study analyzes chaotic systems with infinite attractors using multiscale methods. Complexity depends on initial conditions, with multiscale multivariate permutation entropy showing scale independence, unlike Lempel-Ziv complexity.

Keywords:
chaosmultiscale multivariate entropymultistabilityself-reproducing system

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Information Theory

Background:

  • Designing chaotic systems with infinitely many attractors is a significant challenge in nonlinear dynamics.
  • Understanding the complexity of such systems is crucial for their potential applications.

Purpose of the Study:

  • To analyze the complexity of self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors.
  • To compare the behavior of multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel-Ziv complexity (MMLZC) in characterizing these systems.

Main Methods:

  • Employed multiscale multivariate permutation entropy (MMPE) for complexity analysis.
  • Utilized multiscale multivariate Lempel-Ziv complexity (MMLZC) as a comparative analytical tool.
  • Investigated self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors.

Main Results:

  • The complexity of these chaotic systems is fundamentally determined by their initial conditions.
  • MMPE values were found to be independent of the scale factor.
  • MMLZC exhibited a dependency on the scale factor, distinguishing it from MMPE.

Conclusions:

  • The findings provide a new perspective on characterizing the complexity of chaotic systems with infinite attractors.
  • The scale-independent nature of MMPE offers a distinct advantage for certain analyses.
  • This research serves as a valuable reference for the application of self-reproducing chaotic systems.