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Escape from attracting sets in randomly perturbed systems.

Christian S Rodrigues1, Celso Grebogi, Alessandro P S de Moura

  • 1Max Planck Institute for Mathematics in the Sciences, Inselstr 22, 04103 Leipzig, Germany. christian.rodrigues@mis.mpg.de

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PubMed
Summary
This summary is machine-generated.

This study investigates escape dynamics from attractive states caused by bounded noise, revealing a critical noise threshold for escape and providing analytical escape rate predictions. Numerical simulations validate these findings in chaotic systems.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Science
  • Statistical Physics

Background:

  • Escape dynamics from attractive states are crucial across scientific disciplines.
  • Prior research primarily examined unbounded, Gaussian noise in chaotic systems.
  • The impact of bounded noise on escape dynamics remains less explored.

Purpose of the Study:

  • To investigate escape dynamics induced by bounded noise in chaotic systems.
  • To establish a theoretical framework for understanding escape under bounded perturbations.
  • To derive and validate analytical predictions for escape rates near the transition point.

Main Methods:

  • Formulating an equivalence between bounded noise escape and a closed system with a 'hole'.
  • Developing analytical expressions for escape rate scaling with noise amplitude.
  • Conducting numerical simulations on two-dimensional maps to verify theoretical predictions.

Main Results:

  • Demonstrated a minimum noise amplitude threshold for escape from an attractor's basin.
  • Derived analytical formulas for the scaling of escape rate near the escape transition.
  • Numerical simulations confirmed the accuracy of the derived analytical expressions.

Conclusions:

  • Bounded noise introduces unique escape dynamics distinct from unbounded noise.
  • A critical noise level governs the onset of escape, with predictable scaling.
  • The established equivalence provides a powerful tool for analyzing escape phenomena in various complex systems.