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Strange nonchaotic attractors in random dynamical systems.

Xingang Wang1, Meng Zhan, Choy-Heng Lai

  • 1Temasek Laboratories, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.

Physical Review Letters
|March 5, 2004
PubMed
Summary

Small noise can create strange nonchaotic attractors (SNAs) in various dynamical systems, not just quasiperiodic ones. This finding suggests SNAs are more common in physical and biological applications than previously believed.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Strange nonchaotic attractors (SNAs) were previously thought to primarily exist in quasiperiodically driven systems.
  • Their typical occurrence in other types of dynamical systems remained an open question.
  • Understanding SNA formation is crucial for various physical and biological applications.

Purpose of the Study:

  • To investigate the possibility of inducing robust strange nonchaotic attractors (SNAs) in autonomous and periodically driven systems.
  • To determine if small noise can facilitate the emergence of SNAs in systems beyond quasiperiodic forcing.
  • To broaden the understanding of SNA prevalence in diverse dynamical systems.

Main Methods:

  • Physical analysis of dynamical systems.

Related Experiment Videos

  • Numerical simulations and evidence generation.
  • Investigation of autonomous discrete-time maps.
  • Analysis of periodically driven continuous-time systems under the influence of noise.

    • Main Results:

    • Demonstrated that small amounts of noise can robustly induce strange nonchaotic attractors (SNAs).
    • Confirmed the occurrence of these attractors in both autonomous discrete-time maps and periodically driven continuous-time systems.
    • Provided physical and numerical evidence for SNA induction by noise.

    Conclusions:

    • Strange nonchaotic attractors (SNAs) can be typically induced by small noise in autonomous discrete-time maps and periodically driven continuous-time systems.
    • The findings expand the known conditions for SNA formation.
    • SNAs are likely more common in physical and biological systems than previously assumed.