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Two-dimensional type-I intermittency.

C M Kim1, W H Kye

  • 1National Creative Research Initiative Center for Controlling Optical Chaos, Pai-Chai University, Taejon 302-735, Korea. chmkim@mail.paichai.ae.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study explores two-dimensional intermittency, comparing its channel structure and return map trajectories to one-dimensional intermittency. Numerical results confirm theoretical predictions for scaling relations, offering insights into complex system dynamics.

Area of Science:

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

Background:

  • Intermittency describes systems exhibiting sudden bursts of activity.
  • Understanding intermittency in higher dimensions is crucial for complex system analysis.
  • Previous research primarily focused on one-dimensional systems.

Purpose of the Study:

  • To investigate the general structure of two-dimensional intermittency.
  • To compare channel structures and return map trajectories with one-dimensional intermittency.
  • To derive and verify scaling relations for two-dimensional intermittency.

Main Methods:

  • Analysis of channel structure and trajectory in the return map.
  • Comparison with established models of one-dimensional intermittency.

Related Experiment Videos

  • Numerical simulations of a coupled map system to illustrate temporal behavior and scaling relations.

    • Main Results:

    • Identified distinct channel structures and trajectory patterns in two-dimensional intermittency.
    • Derived scaling relations based on trajectory analysis.
    • Numerical results demonstrated good agreement with theoretical predictions, specifically approximately equal 1/sqrt[epsilon].

    Conclusions:

    • The study provides a framework for understanding two-dimensional intermittency.
    • The derived scaling relations offer quantitative insights into the system's behavior.
    • Confirms the applicability of theoretical predictions to complex dynamical systems.