@Article{Supelec921,
author = {Lionel Weicker and T Erneux and David Rosin and Daniel Gauthier},
title = {{Multirhythmicity in an optoelectronic oscillator with large delay}},
journal = {Physical Review E},
year = {2015},
volume = {91},
number = {012910},
month = {01},
url = {http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.012910},
doi = {http://dx.doi.org/10.1103/PhysRevE.91.012910},
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.}
}