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Related Experiment Videos

Intermingled basins and on-off intermittency in a multistate system

Zhan1, Hu

  • 1Department of Physics, Beijing Normal University, Beijing 100875, China.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

This study explores chaotic dynamics in systems with multiple invariant subspaces. It reveals a transition from intermingled basins to on-off intermittency as a system parameter changes, impacting statistical and transport properties.

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Area of Science:

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

Background:

  • Dynamical systems can exhibit complex behaviors within invariant subspaces.
  • Intermingled basins of attraction are observed between coexisting chaotic states.
  • Parameter variations can lead to transitions in system dynamics.

Purpose of the Study:

  • To investigate the dynamics of a system with infinite low-dimensional symmetric invariant subspaces, each hosting a chaotic state.
  • To analyze the transition from intermingled basin dynamics to multistate on-off intermittency.
  • To examine the statistical behavior and physical transport properties associated with these different dynamic states.

Main Methods:

  • Analysis of dynamical systems with invariant subspaces.

Related Experiment Videos

  • Characterization of chaotic states and basin structures.
  • Calculation of Lyapunov exponents to identify dynamic transitions.
  • Investigation of statistical properties and transport phenomena.

    • Main Results:

    • The system exhibits infinite symmetric invariant subspaces, each with a chaotic state.
    • Stable chaotic states lead to intermingled basins.
    • A transition from intermingled basins to multistate on-off intermittency occurs as the transverse Lyapunov exponent becomes positive.
    • Detailed analysis of statistical behavior and physical transport for different dynamic states.

    Conclusions:

    • The study elucidates the complex interplay between invariant subspaces, chaotic dynamics, and parameter-driven transitions.
    • The findings provide insights into the mechanisms governing intermingled basins and on-off intermittency.
    • Understanding these dynamics is crucial for predicting statistical behavior and transport properties in complex systems.