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Two distinct bifurcation routes for delayed optoelectronic oscillators.
Lionel Weicker1,2, Gaetan Friart3, Thomas Erneux3
1Chair in Photonics, LMOPS, CentraleSupélec, Université Paris-Saclay, F-57070 Metz, France.
Physical Review. E
|January 20, 2018
Summary
This study explores how low- and high-frequency oscillations coexist in a delayed optoelectronic oscillator. Researchers found two distinct Hopf bifurcation points that lead to stable solutions, even when instabilities arise.
Area of Science:
- Nonlinear dynamics
- Optoelectronics
- Complex systems
Background:
- Delayed optoelectronic oscillators exhibit complex behaviors.
- Understanding oscillation coexistence is crucial for controlling such systems.
Purpose of the Study:
- Investigate the coexistence of low- and high-frequency oscillations.
- Analyze the stability of these oscillations around Hopf bifurcation points.
- Explore the impact of feedback rate on solution branches.
Main Methods:
- Analytical demonstration of stable solutions near Hopf bifurcations.
- Numerical simulations to observe higher-order instabilities.
- Bifurcation analysis to track solution paths.
Main Results:
- Identified two nearby Hopf bifurcation points for low- and high-frequency oscillations.
- Demonstrated analytical pathways to stable solutions.
- Observed that solution branches remain separated despite instabilities at higher feedback rates.
Conclusions:
- The coexistence of low- and high-frequency oscillations is supported by distinct Hopf bifurcation routes.
- These routes are robust and can be independently navigated by adjusting the bifurcation parameter.
- The findings offer insights into controlling complex dynamics in delayed systems.
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