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Why are chaotic attractors rare in multistable systems?

Ulrike Feudel1, Celso Grebogi

  • 1ICBM, Universität Oldenburg, Germany.

Physical Review Letters
|October 4, 2003
PubMed
Summary

Chaotic attractors are seldom found in multistable dissipative systems near the conservative limit. As this limit is approached, chaotic attractors and their basins rapidly shrink, disappearing via double crises.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Statistical Physics

Background:

  • Multistable dissipative systems exhibit complex dynamics.
  • Understanding the conditions for chaotic attractors is crucial.
  • The behavior near the conservative limit is of particular interest.

Purpose of the Study:

  • Investigate the prevalence of chaotic attractors in multistable dissipative systems.
  • Analyze the disappearance of chaotic attractors and their basins of attraction.
  • Identify the mechanisms driving the vanishing of chaotic dynamics.

Main Methods:

  • Numerical simulations of multistable dissipative systems.
  • Analysis of parameter space and state space volumes.
  • Characterization of crises and basin boundary metamorphoses.

Main Results:

  • Chaotic attractors are rare in multistable dissipative systems close to the conservative limit.
  • Parameter intervals and basin volumes shrink rapidly as the conservative limit is approached.
  • Double crises, involving basin boundary metamorphosis, are key to attractor disappearance.
  • Scaling relations for successive double crises and attractor disappearance were established.

Conclusions:

  • The transition to conservative systems leads to the suppression of chaotic attractors.
  • Double crises represent a critical phenomenon governing the loss of chaotic dynamics.
  • Scaling laws provide a quantitative description of chaotic attractor vanishing.

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