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Noise-induced dynamics in bistable systems with delay.

L S Tsimring1, A Pikovsky

  • 1Institute for Nonlinear Science, University of California-San Diego, La Jolla, California 92093-0402, USA.

Physical Review Letters
|December 12, 2001
PubMed
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This study explores noise-induced dynamics in bistable systems with delayed feedback, revealing a coherence resonance phenomenon. The system

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Stochastic Processes

Background:

  • Bistable systems are fundamental in various scientific fields.
  • Delayed feedback introduces complex dynamics.
  • Noise can significantly alter system behavior.

Purpose of the Study:

  • Investigate noise-induced dynamics in a bistable system with delayed feedback.
  • Analyze the influence of feedback delay on system behavior.
  • Explore the phenomenon of coherence resonance.

Main Methods:

  • Theoretical analysis of a two-state model with state-dependent transition rates.
  • Numerical simulations to study system dynamics.
  • Derivation of analytical solutions for autocorrelation function and power spectrum.

Related Experiment Videos

Main Results:

  • Identified a peak in the power spectrum at a frequency related to the inverse delay time.
  • Observed that the power spectrum's amplitude peaks at a specific noise level, demonstrating coherence resonance.
  • Found that linear response to periodic forcing exhibits maxima at frequencies related to the inverse delay time and its harmonics.

Conclusions:

  • Delayed feedback in bistable systems can lead to noise-enhanced phenomena like coherence resonance.
  • The system's response is tunable by noise level and feedback delay.
  • Findings have implications for understanding and controlling stochastic systems with memory.