Slow–fast dynamics of a time-delayed electro-optic oscillator | Zendy

Lionel Weicker | Zendy; Thomas Erneux | Zendy; Otti D’Huys | Zendy; Jan Danckaert | Zendy; Maxime Jacquot | Zendy; Yanne K. Chembo | Zendy; Laurent Larger | Zendy

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Slow–fast dynamics of a time-delayed electro-optic oscillator

Author(s) -

Lionel Weicker,

Thomas Erneux,

Otti D’Huys,

Jan Danckaert,

Maxime Jacquot,

Yanne K. Chembo,

Laurent Larger

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0459

Subject(s) - hopf bifurcation , bifurcation , bifurcation diagram , plateau (mathematics) , square (algebra) , square wave , steady state (chemistry) , physics , mathematics , period (music) , diagram , mathematical analysis , mechanics , geometry , quantum mechanics , chemistry , nonlinear system , statistics , voltage , acoustics

International audienceSquare-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

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