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Externally controlled attractor selection in a high-dimensional system.

Frederick H Willeboordse1, Kunihiko Kaneko

  • 1Department of Physics, The National University of Singapore, Singapore 119260. willeboordse@yahoo.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
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This study shows external inputs can control complex dynamical systems with many attractors. Researchers demonstrated attractor selection by adjusting noise duration or parameter sweeping speed.

Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Control Theory

Background:

  • Investigating high-dimensional dynamical systems with numerous attractors, analogous to memory systems.
  • Understanding the inherent controllability of such complex systems.

Purpose of the Study:

  • To demonstrate the controllability of a high-dimensional dynamical system with global couplings.
  • To explore methods for selecting specific attractors within this system using external inputs.

Main Methods:

  • Utilizing external inputs to manipulate the system's dynamics.
  • Varying the duration of added noise to influence attractor selection.
  • Controlling the sweeping speed of a parameter to achieve attractor selection.

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Main Results:

  • Demonstrated that external inputs can control the selection of final attractors.
  • Showed that attractor selection is achievable by modulating noise duration as degrees of freedom decrease.
  • Confirmed attractor selection is also possible by controlling parameter sweeping speed.
  • Explained the general mechanism underlying this controlled attractor selection.

Conclusions:

  • The investigated system serves as a prototype for understanding memory-like systems with vast attractor landscapes.
  • Controlled attractor selection is a general mechanism applicable to various complex systems.
  • The findings have direct applications in attractor switching phenomena.