  The effect of time-delayed coupling on the collective behavior of a
population of globally coupled complex Ginzburg-Landau (GCCGL) oscillators is
investigated. A detailed numerical study is carried out to study the impact of
time delay on various collective states that include synchronous states,
multicluster states, chaos, amplitude mediated chimeras and incoherent states.
It is found that time delay can bring about significant changes in the
dynamical properties of these states including their regions of existence and
stability. In general, an increase in time delay is seen to lower the threshold
value of the coupling strength for the occurrence of such states and to shift
the existence domain towards more negative values of the linear dispersion
parameter. Further insights into the numerical findings are provided, wherever
possible, by exact equilibrium and stability analysis of these states in the
presence of time delay.
