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Riddled-like basins of transient chaos

Woltering1, Markus

  • 1Max Planck Institut fur Molekulare Physiologie, Postfach 500247, 44202 Dortmund, Germany.

Physical Review Letters
|October 4, 2000
PubMed
Summary
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Transient chaos near a crisis point exhibits riddled-like behavior, even with limited accuracy. This phenomenon, observed in both mathematical models and chemical reactions, is practically indistinguishable from riddled basins due to finite precision.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Chemical kinetics

Background:

  • Transient chaos occurs in dynamical systems near a crisis.
  • Riddled basins are a complex dynamical phenomenon where initial conditions are intricately mixed.
  • Finite accuracy in measurements and computations is a practical limitation.

Purpose of the Study:

  • To investigate the presence of riddled-like behavior in the initial conditions of transient chaos.
  • To determine if this behavior persists under finite accuracy constraints.
  • To compare this phenomenon with established riddled basin dynamics.

Main Methods:

  • Numerical simulations using the logistic map.
  • Modeling a quantitatively described chemical reaction.

Related Experiment Videos

  • Analysis of initial condition sets under varying precision levels.

    • Main Results:

    • Transient chaos near a crisis point demonstrates riddled-like behavior for any finite accuracy.
    • This apparent riddling is computationally and experimentally indistinguishable from true riddled basins.
    • The findings hold for both abstract mathematical models and realistic chemical systems.

    Conclusions:

    • Finite accuracy in computational or experimental settings leads to observable riddled-like behavior in transient chaos.
    • This behavior mimics riddled basins, posing challenges for precise system analysis.
    • The study highlights the practical implications of precision limitations in chaos studies.