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

The effects of uncorrelated white noise on a series of Josephson junctions coupled to a linear RLC resonator are investigated. Both the cases of identical and nonidentical parameters are considered. The junctions are hysteretic, and hence can be considered birhythmic; that is, capable of oscillating at different frequencies for the same set of parameters. It is also found that, in the presence of noise, a uniform array behaves similarly to a single Josephson junction. However, 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 birhythmic properties for large values of the variance of the disorder parameter and remains birhythmic only 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.