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Slow-fast dynamics of a time-delayed electro-optic oscillator.
Lionel Weicker1, Thomas Erneux, Otti D'Huys
1Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, CP 231, 1050 Brussels, Belgium.
Summary
This study analyzes the fast transition layers in electro-optic oscillator square waves, revealing their contribution to the oscillation period. It also explores bifurcation diagrams, showing square waves emerge from Hopf bifurcations and can coexist with other stable oscillations.
Area of Science:
- Nonlinear Dynamics
- Optics and Photonics
Background:
- Experimental observation of square-wave oscillations with varying plateau lengths in electro-optic oscillators.
- Previous analysis of model delay differential equations yielding asymptotic approximations for plateaus.
Purpose of the Study:
- Investigate the role of fast transition layers between plateaus in determining the total period of square-wave oscillations.
- Analyze the bifurcation diagram to understand the emergence and coexistence of stable solutions.
Main Methods:
- Analysis of model delay differential equations.
- Investigation of fast transition layers and their contribution to the oscillation period.
- Bifurcation analysis of stable solutions.
Main Results:
- Characterization of fast transition layers and their impact on the total period of square-wave oscillations.
- Demonstration that square waves originate from the first Hopf bifurcation of the steady state.
- Identification of coexistence between stable square waves and low-frequency periodic oscillations for identical control parameters.
Conclusions:
- Fast transition layers are crucial for understanding the period of electro-optic oscillator square waves.
- The emergence of square waves is linked to Hopf bifurcations, with potential for multiple stable states.
- Bifurcation analysis provides insights into the complex dynamics and parameter-dependent behavior of these oscillators.
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