Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 371, Issue 1999, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2012.0459
Keywords
oscillations; dynamics; time delay; square waves; Hopf bifurcation
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Funding
- FNRS (Belgium)
- Belgian FRIA
- Belgian Science Policy Office [IAP-7/35]
- European project PHOCUS FP7 grant [240763]
- Institut Universitaire de France
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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.
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