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Perturbed on-off intermittency.

D Marthaler1, D Armbruster, Y C Lai

  • 1Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
PubMed
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On-off intermittency requires an invariant subspace. Perturbations destroying this subspace cause abrupt changes in scaling laws for measurable quantities, altering intermittency behavior.

Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • On-off intermittency is a phenomenon observed in dynamical systems.
  • A fundamental prerequisite for on-off intermittency is the existence of an invariant subspace.
  • The behavior of such systems under perturbations is not fully understood.

Purpose of the Study:

  • To investigate the manifestation of on-off intermittency when an invariant subspace is destroyed by a perturbation.
  • To differentiate between experimental measurement thresholds relative to perturbation size.
  • To characterize the changes in scaling laws due to perturbations.

Main Methods:

  • Geometric analysis of system dynamics.
  • Development of a random-walk model to simulate intermittency.

Related Experiment Videos

  • Numerical computations to validate theoretical findings.

    • Main Results:

    • Perturbations destroying the invariant subspace lead to a metamorphosis of on-off intermittency.
    • Scaling laws for physically measurable quantities change abruptly as the perturbation parameter increases.
    • The relationship between perturbation size and measurement threshold influences the observed intermittency.

    Conclusions:

    • The presence and integrity of invariant subspaces are critical for standard on-off intermittency.
    • Perturbations induce qualitative changes in the scaling behavior of intermittent systems.
    • Understanding these changes is crucial for interpreting experimental and numerical results in nonlinear dynamics.