title: Slow-fast dynamics of a time-delayed electro-optic oscillator.
abstract: Square-wave oscillations exhibiting different plateau lengths have been observed experimentally by investigating an electro-optic oscillator. In a previous study, we analysed the model delay differential equations and determined an asymptotic approximation of the two plateaus. In this paper, we concentrate on the fast transition layers between plateaus and show how they contribute to the total period. We also investigate the bifurcation diagram of all possible stable solutions. We show that the square waves emerge from the first Hopf bifurcation of the basic steady state and that they may coexist with stable low-frequency periodic oscillations for the same value of the control parameter.
authors: Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, CP 231, 1050 Brussels, Belgium.
authors: Lionel
authors: L
authors: Weicker
authors: Thomas
authors: T
authors: Erneux
authors: Otti
authors: O
authors: D'Huys
authors: Jan
authors: J
authors: Danckaert
authors: Maxime
authors: M
authors: Jacquot
authors: Yanne
authors: Y
authors: Chembo
authors: Laurent
authors: L
authors: Larger
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D009991:Oscillometry / Q000379:methods*
keywords: Hopf bifurcation; dynamics; oscillations; square waves; time delay