  We investigate the emergence of chimera and cluster states possessing
asymmetric dynamics in globally coupled systems, where the trajectories of
oscillators belonging to different subpopulations exhibit different dynamical
properties. In an asymmetric chimera state, the trajectory of an element in the
synchronized subset is stationary or periodic, while that of an oscillator in
the desynchronized subset is chaotic. In an asymmetric cluster state, the
periods of the trajectories of elements belonging to different clusters are
different. We consider a network of globally coupled chaotic maps as a simple
model for the occurrence of such asymmetric states in spatiotemporal systems.
We employ the analogy between a single map subject to a constant drive and the
effective local dynamics in the globally coupled map system to elucidate the
mechanisms for the emergence of asymmetric chimera and cluster states in the
latter system. By obtaining the dynamical responses of the driven map, we
establish a condition for the equivalence of the dynamics of the driven map and
that of the system of globally coupled maps. This condition is applied to
predict parameter values and subset partitions for the formation of asymmetric
cluster and chimera states in the globally coupled system.
