In order to describe properly the magnetic status of a 2D superconducting junction array, one has to consider not only the effect of the screening currents but also that of the particular experimental protocol followed to measure the physical quantities of interest like, for example, the magnetization. We show that the value of the lower critical field, f~l, of the junction array depends strongly on the intensity of the screening currents, i.e. on the strength of the junction coupling, Ej, and that reliable results can be obtained only by considering the full-inductance matrix. We also show that the magnetic configuration of the vortices may depend on the particular experimental approach followed (static or dynamic) and, even, in some cases, on the initial configuration of the phases.

The domains of dynamical coherence (i.e. the Shapiro step-plateaus) observable when an array of overdamped Josephson junctions is subjected to an external periodic perturbation, can be strongly modified by the presence of both the disorder and the frustration, f. In particular, by varying the value off it is possible to induce a reduction in the width of the integer giant Shapiro step-plateaus (corresponding to a compression of the attraction basin of the main locked states of the system) and the progressive appearance of a subharmonic devil staircase characterized by a fractal dimension, D = 0.88, value that agrees with what has been observed for other complex systems. The sensitivity of the I-V characteristics to f is mirrored in the complexity of the dynamical phase space composed by phase-locked domains separated by regions of chaotic dynamics.

We present a detailed investigation of the role played by the areal (positional) disorder and by frustration, f, in determining the properties of the 2D arrays of superconducting junctions in the range of large f. Our computer simulations show, as expected, the existence of periodic structures in the energy vs. f plots. However, the amplitude decay of these structures, induced by the areal disorder, is not linear with f. A similar conclusion can be drawn by inspecting the magnetic moment vs. f plots. By means of a non-linear extrapolation, we are able to define a crossover field, fc, beyond which the phases of the junctions appear to be randomly oriented. The value of the crossover field scales almost linearly with the inverse of the degree of disorder, but the slope does not take the universal value, 0.34, previously proposed. The crossover to the glassy phase, with increasing f, simply mirrors the reaching of the saturation value in the continuously increasing width of the distribution of the plaquette current circuitation.

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