Controlled generation of chimera states in SQUID metasurfaces using DC flux gradients

SQUID (Superconducting QUantum Interference Device) metasurfaces, subject to a time-independent (dc) flux gradient and driven by a sinusoidal (ac) flux field, support chimera states that can be generated with zero initial conditions. The dc flux gradient and the amplitude of the ac flux can thus control the number of desynchronized clusters of such a generated chimera state (i.e., its “heads”) as well as their location and size. The combination of three measures, i.e., the synchronization parameter averaged over the period of the driving flux, the strength of incoherence, and the discontinuity measure, is used to predict the emergence or not of a chimera state and its multiplicity on the parameter plane of the dc flux gradient and the ac flux amplitude. Moreover, the full-width half-maximum of the distribution of the values of the synchronization parameter averaged over the period of the ac driving flux, allows to distinguish chimera states from non-chimera, partially synchronized states. Our findings are relevant from the pointview of both theory and applications. The SQUID oscillator provides an excellent physical example of systems with inertia and driving, for which chimera states have been under-examined. Finally, in the parameter regime under consideration, SQUID lattices are systems which are experimentally realisable and have very important applications in metamaterials science.