  A system of two identical SQUIDs (superconducting quantum interference
devices) symmetrically coupled through their mutual inductance and driven by a
sinusoidal field is investigated numerically with respect to dynamical
properties such as its multibranched resonance curve, its bifurcation
structure, as well as its synchronization behavior. The SQUID dimer is found to
exhibit a hysteretic resonance curve with a bubble connected to it through
Neimark-Sacker (torus) bifurcations, along with coexisting chaotic branches in
their vicinity. Interestingly, the transition of the SQUID dimer to chaos
occurs through a period-doubling cascade of a two-dimensional torus
(quasiperiodicity-to-chaos transition). The chaotic states are identified
through the calculated Lyapunov spectrum, and their basins of attraction have
been determined. Bifurcation diagrams have been constructed on the parameter
plane of the coupling strength and the driving frequency of the applied field,
and they are superposed to maps of the maximum Lyapunov exponent on the same
plane. In this way, a clear connection between chaotic behavior and torus
bifurcations is revealed. Moreover, asymmetric states that resemble localized
synchronization have been detected using the correlation function between the
fluxes threading the loop of the SQUIDs. The effect of intermittent chaotic
synchronization, which seems to be present in the SQUID dimer, is only slightly
touched.
