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Related Experiment Videos

Controlling global stochasticity in the standard map.

Y Zhang1, Y Yao

  • 1LCP, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009(26), Beijing 100088, People's Republic of China.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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A new method controls global stochasticity in 2D Hamiltonian systems, stabilizing chaotic motion. This approach remains effective even with external noise, revealing a novel intermittency pattern under high noise levels.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • Controlling stochasticity in Hamiltonian systems is crucial for understanding complex dynamics.
  • The standard map model is a fundamental tool for studying chaos in two-dimensional systems.

Purpose of the Study:

  • To propose and validate a novel method for controlling global stochasticity in two-dimensional Hamiltonian systems.
  • To investigate the robustness of this control method in the presence of external noise.

Main Methods:

  • Modeling the standard map to demonstrate the control technique.
  • Analyzing the system's behavior under varying noise strengths.

Main Results:

  • The proposed method successfully stabilizes global stochasticity into regular motion within localized regions.

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  • The control is robust against weak external noise.
  • Large noise strengths induce a new type of intermittency, termed noise-induced intermittency, similar to in-out intermittency.

    • Conclusions:

    • A practical method for controlling chaos in two-dimensional Hamiltonian systems has been developed.
    • The study reveals a new noise-induced intermittency phenomenon with implications for understanding complex systems.
    • The findings contribute to the broader understanding of chaos control and noise effects in dynamical systems.