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This paper deal the effects of uncorrelated white noise, in a serie ofJosephson Junctions coupled to a linear $RLC$ resonator. The junction arehysteretic, and hence can be considered birhythmic, that is capable tooscillate at different frequencies for the same set of parameters. BothJosephson Junctions with identical and disordered parameters are considered.With the uniform parameters, the array behaves similarly to single Josephsonjunctions, also in the presence of noise. The magnitude of the effective energythat characterizes the response to noise becomes smaller as the number ofelements of the array increases, making the resonator less stable. Disorder inthe parameters drastically changes the physics of the array. The disorderedarray of Josephson junctions misses the birhythmicity properties for largevalues of the variance of the disorder parameter. Nevertheless, the systemremains birhythmic for low values of the disorder parameter. Finally, disordermakes it difficult to locate the separatrix, hinting to a more complexstructure of the effective energy landscape.

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