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The existence and stability of dissipative discrete breathers (DDBs) in rfsuperconducting quantum interference device (SQUID) arrays in both one and twodimensions is investigated numerically. In an rf SQUID array, the nonlinearitywhich is intrinsic to each SQUID due to the presence of the Josephson junction(on-site nonlinearity), along with the weak coupling of each SQUID to itsnearest neighbors through magnetic forces, result in the appearance of discretebreathers. We analyze several discrete breather excitations, both in one andtwo dimensions, which are subjected to unavoidable losses. These losses,however, are counter-balanced by an external flux source leading to linearlystable discrete breather structures up to relatively large coupling parameters.We show that DDB excitations may locally alter the magnetic response of arrayfrom paramagnetic to diamagnetic or vice versa, and that they are not destroyedby increasing the dimensionality.

Dissipative discrete breathers in rf SQUID metamaterials