  We investigate the influence of time-delayed coupling in a ring network of
non-locally coupled Stuart-Landau oscillators upon chimera states, i.e.,
space-time patterns with coexisting partially coherent and partially incoherent
domains. We focus on amplitude chimeras which exhibit incoherent behavior with
respect to the amplitude rather than the phase and are transient patterns, and
show that their lifetime can be significantly enhanced by coupling delay. To
characterize their transition to phase-lag synchronization (coherent traveling
waves) and other coherent structures, we generalize the Kuramoto order
parameter. Contrasting the results for instantaneous coupling with those for
constant coupling delay, for time-varying delay, and for distributed-delay
coupling, we demonstrate that the lifetime of amplitude chimera states and
related partially incoherent states can be controlled, i.e., deliberately
reduced or increased, depending upon the type of coupling delay.
