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Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator.

Authors
  • Weicker, Lionel
  • Erneux, Thomas
  • Jacquot, Maxime
  • Chembo, Yanne
  • Larger, Laurent
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Feb 01, 2012
Volume
85
Issue
2 Pt 2
Pages
26206–26206
Identifiers
PMID: 22463299
Source
Medline
License
Unknown

Abstract

An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.

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