title: Strongly asymmetric square waves in a time-delayed system.
abstract: Time-delayed systems are known to exhibit symmetric square waves oscillating with a period close to twice the delay. Here, we show that strongly asymmetric square waves of a period close to one delay are possible. The plateau lengths can be tuned by changing a control parameter. The problem is investigated experimentally and numerically using a simple bandpass optoelectronic delay oscillator modeled by nonlinear delay integrodifferential equations. An asymptotic approximation of the square-wave periodic solution valid in the large delay limit allows an analytical description of its main properties (extrema and square pulse durations). A detailed numerical study of the bifurcation diagram indicates that the asymmetric square waves emerge from a Hopf bifurcation.
authors.affiliation: Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium.
authors.forename: Lionel
authors.initials: L
authors.lastname: Weicker
authors.forename: Thomas
authors.initials: T
authors.lastname: Erneux
authors.forename: Otti
authors.initials: O
authors.lastname: D'Huys
authors.forename: Jan
authors.initials: J
authors.lastname: Danckaert
authors.forename: Maxime
authors.initials: M
authors.lastname: Jacquot
authors.forename: Yanne
authors.initials: Y
authors.lastname: Chembo
authors.forename: Laurent
authors.initials: L
authors.lastname: Larger
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D009991:Oscillometry / Q000379:methods*