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Intermingled basins due to finite accuracy

Schmick1, Goles, Markus

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

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Even with high accuracy, chaotic systems with attracting points exhibit indistinguishable basins of attraction. Bifurcations lead to on-off intermittency, causing state alternations between frozen and gaslike dynamics.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Statistical Mechanics

Background:

  • Chaotic systems often exhibit complex dynamics and attractors.
  • Dissipation can lead to distinct attracting configurations in physical systems.
  • Bifurcations can drastically alter system behavior.

Purpose of the Study:

  • To numerically investigate the basin structure of two distinct chaotic systems.
  • To analyze the phenomenon of on-off intermittency induced by bifurcations.
  • To characterize the resulting state alternations in a dissipative system.

Main Methods:

  • Numerical simulations of a chaotic map with attracting points.
  • Modeling of colliding disks in a periodically tilted box with dissipation.
  • Analysis of phase space and basin boundaries for finite accuracy.

Related Experiment Videos

  • Investigation of bifurcations leading to state transitions.

    • Main Results:

    • For finite accuracy, basins of attraction become indistinguishable, mimicking intermingled basins.
    • Any neighborhood contains points leading to different attractors.
    • Bifurcations induce on-off intermittency, characterized by alternating 'frozen' and gaslike states.

    Conclusions:

    • Finite accuracy fundamentally limits the distinguishability of basins in these chaotic systems.
    • On-off intermittency is a key phenomenon arising from bifurcations in dissipative chaotic systems.
    • The study highlights the complex interplay between chaos, dissipation, and bifurcations in determining system dynamics.