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Multirhythmicity in an optoelectronic oscillator with large delay.

Lionel Weicker1, Thomas Erneux2, David P Rosin3

  • 1Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Bruxelles, Belgium and Applied Physics Research Group (APHY), Vrije Universiteit Brussel, 1050 Brussels, Belgium and OPTEL Research Group, CentraleSupélec, LMOPS (EA 4423), 2 rue Édouard Belin, 57070 Metz, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
PubMed
Summary

This study explores optoelectronic oscillators with large feedback delays, revealing coexisting square-wave oscillations (multirhythmicity). Different phase shifts lead to distinct oscillation periods, validated by experiments and theory.

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Area of Science:

  • Nonlinear dynamics
  • Optoelectronics
  • Complex systems

Background:

  • Optoelectronic oscillators are crucial in signal processing and communication.
  • Large feedback delays can introduce complex dynamical behaviors.
  • Understanding multirhythmicity is key to controlling oscillator outputs.

Purpose of the Study:

  • To investigate the phenomenon of multirhythmicity in an optoelectronic oscillator with a large delay.
  • To theoretically and experimentally characterize the coexisting square-wave oscillation regimes.
  • To analyze the emergence and stability of these periodic solutions.

Main Methods:

  • Experimental setup of an optoelectronic oscillator with a significant feedback loop delay.
  • Theoretical modeling using nonlinear dynamical systems analysis.
  • Numerical simulations to replicate experimental observations.
  • Linear stability analysis of periodic solutions using fixed-point mapping.

Main Results:

  • Demonstration of multiple coexisting square-wave oscillation patterns (multirhythmicity) for identical parameters.
  • Identification of two distinct types of periodic regimes based on phase shift: integer fractions of the delay or odd integer fractions of twice the delay.
  • Quantitative agreement between experimental data and theoretical/numerical predictions.
  • Analysis of periodic solutions emerging from Hopf bifurcations and stabilizing via an Eckhaus-like instability.

Conclusions:

  • The study confirms the existence and characteristics of multirhythmicity in delayed optoelectronic oscillators.
  • The findings provide insights into the mechanisms governing complex dynamics and stability in such systems.
  • The results offer a foundation for designing and controlling oscillators with specific periodic behaviors.