Noise and disorder effects in a series of birhythmic Josephson junctions coupled to a resonator

This paper deal the effects of uncorrelated white noise, in a serie of Josephson Junctions coupled to a linear $RLC$ resonator. The junction are hysteretic, and hence can be considered birhythmic, that is capable to oscillate at different frequencies for the same set of parameters. Both Josephson Junctions with identical and disordered parameters are considered. With the uniform parameters, the array behaves similarly to single Josephson junctions, also in the presence of noise. The magnitude of the effective energy that characterizes the response to noise becomes smaller as the number of elements of the array increases, making the resonator less stable. Disorder in the parameters drastically changes the physics of the array. The disordered array of Josephson junctions misses the birhythmicity properties for large values of the variance of the disorder parameter. Nevertheless, the system remains birhythmic for low values of the disorder parameter. Finally, disorder makes it difficult to locate the separatrix, hinting to a more complex structure of the effective energy landscape.