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Attractor bifurcation and on-off intermittency.

W H Kye1, D Topaj

  • 1Department of Physics, Potsdam University, Am Neuen Palais, PF 601553, D-14415 Potsdam, Germany. whkye@yahoo.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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Bifurcation phenomena in coupled map systems are characterized by on-off intermittency. This study rigorously describes this using a virtually invariant manifold concept, supported by numerical results.

Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Coupled map lattices exhibit complex dynamical behaviors.
  • Bifurcation phenomena are critical for understanding system transitions.
  • On-off intermittency is a known chaotic behavior characterized by bursts of activity.

Purpose of the Study:

  • To analyze the bifurcation of attractors in multiplicatively coupled map systems.
  • To characterize this bifurcation using on-off intermittency.
  • To provide a rigorous description of the phenomenon using the concept of a virtually invariant manifold.

Main Methods:

  • Analysis of multiplicatively coupled map systems.
  • Characterization using on-off intermittency.
  • Application of the virtually invariant manifold concept.

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  • Numerical simulations to validate theoretical claims.

    • Main Results:

    • The bifurcation of an attractor in the studied system is shown to be characterized by on-off intermittency.
    • On-off intermittency in the presence of noise is rigorously described.
    • Numerical results confirm the proposed characterization and description.

    Conclusions:

    • On-off intermittency plays a crucial role in the bifurcation phenomena of coupled map systems.
    • The concept of a virtually invariant manifold provides a rigorous framework for describing noisy on-off intermittency.
    • This work elucidates the interplay between bifurcation, intermittency, and noise in complex systems.