title: Multirhythmicity in an optoelectronic oscillator with large delay.
abstract: An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square waves is substantiated analytically by determining the stable fixed points of a map.
authors: Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Bruxelles, Belgium and Applied Physics Research Group (APHY), Vrije Universiteit Brussel, 1050 Brussels, Belgium and OPTEL Research Group, CentraleSupélec, LMOPS (EA 4423), 2 rue Édouard Belin, 57070 Metz, France.
authors: Lionel
authors: L
authors: Weicker
authors: Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, CP 231, 1050 Bruxelles, Belgium.
authors: Thomas
authors: T
authors: Erneux
authors: Department of Physics, Duke University, Durham, North Carolina 27708, USA.
authors: David P
authors: DP
authors: Rosin
authors: Department of Physics, Duke University, Durham, North Carolina 27708, USA.
authors: Daniel J
authors: DJ
authors: Gauthier