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Escaping from nonhyperbolic chaotic attractors.

Suso Kraut1, Celso Grebogi

  • 1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 Sao Paulo, Brazil.

Physical Review Letters
|July 13, 2004
PubMed
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Noise-induced escape from chaotic attractors is explained by a general mechanism involving homoclinic tangency. This study clarifies escape dynamics in low noise limits using Hamiltonian theory, applicable to various systems.

Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Statistical Physics

Background:

  • Understanding noise-induced escape from chaotic systems is crucial for physics and engineering.
  • Nonhyperbolic chaotic attractors present unique challenges in escape dynamics.

Purpose of the Study:

  • To uncover the general mechanism of noise-induced escape from nonhyperbolic chaotic attractors.
  • To establish the role of homoclinic tangency in the escape process.
  • To provide a theoretical framework applicable to low noise limits.

Main Methods:

  • Utilizing the Hamiltonian theory of large fluctuations.
  • Solving variational equations derived from Hamiltonian theory.
  • Applying the theory to paradigmatic systems like the Hénon and Ikeda maps.

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Main Results:

  • Identified a general mechanism for noise-induced escape in the low noise limit.
  • Established the critical role of the primary homoclinic tangency near the basin boundary.
  • Provided an unambiguous solution for the relevant variational equations.

Conclusions:

  • The findings offer a fundamental understanding of escape dynamics from nonhyperbolic chaotic attractors.
  • The developed theory is applicable to driven flow systems and experimental data analysis.
  • Homoclinic tangency is a key dynamical feature governing escape.