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Synchronization of noisy delayed feedback systems with delayed coupling.

Nikola Burić1, Kristina Todorović, Nebojsa Vasović

  • 1Institute of Physics, University of Beograd, PO Box 68, 11080 Beograd-Zemun, Serbia. buric@phy.bg.ac.yu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary

This study demonstrates that delayed coupled Ikeda oscillators achieve exact synchronization in the mean with multiplicative noise when coupling is sufficiently strong. An analytic estimate for this coupling strength is provided and validated numerically.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Stochastic Systems

Background:

  • Investigating synchronization in coupled nonlinear oscillators is crucial for understanding complex systems.
  • Delayed feedback and stochastic perturbations introduce significant challenges to synchronization phenomena.
  • Ikeda oscillators serve as a relevant model for studying chaotic dynamics and synchronization.

Purpose of the Study:

  • To analyze the synchronization of delayed coupled Ikeda oscillators under stochastic perturbations and delayed nonlinear feedback.
  • To determine the conditions for achieving exact synchronization in the mean.
  • To provide an analytic estimate for the required coupling strength.

Main Methods:

  • Utilizing theoretical analysis to prove synchronization conditions.
  • Employing mathematical modeling of circular chains of three and four delayed coupled Ikeda oscillators.
  • Conducting numerical computations to compare with analytic results and illustrate noise effects.

Main Results:

  • Exact synchronization in the mean is proven to occur for sufficiently large coupling in the presence of multiplicative noise.
  • An analytic estimate for the sufficient coupling strength is derived.
  • Numerical computations confirm the analytic findings and illustrate noise-induced synchronization behaviors.

Conclusions:

  • Sufficiently strong coupling can overcome noise and achieve synchronization in delayed nonlinear systems.
  • The derived analytic estimate provides a valuable criterion for predicting synchronization.
  • Understanding the interplay between delay, noise, and coupling is essential for controlling complex system dynamics.