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An optoelectronic oscillator exhibiting a large delay in its feedback loop isstudied both experimentally and theoretically. We show that multiplesquare-wave oscillations may coexist for the same values of the parameters(multirhythmicity). Depending on the sign of the phase shift, these regimesadmit either periods close to an integer fraction of the delay or periods closeto an odd integer fraction of twice the delay. These periodic solutions emergefrom successive Hopf bifurcation points and stabilize at a finite amplitudefollowing a scenario similar to Eckhaus instability in spatially extendedsystems. We find quantitative agreements between experiments and numericalsimulations. The linear stability of the square-waves is substantiatedanalytically by determining stable fixed points of a map.

Multirhythmicity in an optoelectronic oscillator with large delay