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Controlling hamiltonian chaos by adaptive integrable mode coupling

Zhang1, Chen, Yao

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

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

This study introduces a new method to control chaos in two-dimensional Hamiltonian systems. The adaptive integrable mode coupling method stabilizes chaotic motion, removing global stochasticity from the phase space.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Hamiltonian systems often exhibit complex chaotic behavior.
  • Controlling chaos is crucial for understanding and predicting system dynamics.

Purpose of the Study:

  • To propose and demonstrate an adaptive integrable mode coupling method for controlling two-dimensional Hamiltonian chaos.
  • To stabilize chaotic motions into regular ones.

Main Methods:

  • Adaptive integrable mode coupling method.
  • Application to a model of the standard map.

Main Results:

  • The proposed control method successfully stabilizes chaotic motions.
  • Global stochasticity in the phase space can be eliminated by switching the control on and off.

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Conclusions:

  • The adaptive integrable mode coupling method is effective for controlling two-dimensional Hamiltonian chaos.
  • This technique offers a way to remove global stochasticity, leading to more predictable system behavior.