  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.
