  We investigate the effect of repulsive coupling together with an attractive
coupling in a network of nonlocally coupled oscillators. To understand the
complex interaction between these two couplings we introduce a control
parameter in the repulsive coupling which plays a crucial role in inducing
distinct complex collective patterns. In particular, we show the emergence of
various cluster chimera death states through a dynamically distinct transition
route, namely the oscillatory cluster state and coherent oscillation death
state as a function of the repulsive coupling in the presence of the attractive
coupling. In the oscillatory cluster state, the oscillators in the network are
grouped into two distinct dynamical states of homogeneous and inhomogeneous
oscillatory states. Further, the network of coupled oscillators follows the
same transition route in the entire coupling range. Depending upon distinct
coupling ranges the system displays a different number of clusters in the death
state and oscillatory state. We also observe that the number of coherent
domains in the oscillatory cluster state exponentially decreases with increase
in coupling range and obeys a power law decay. Additionally, we show analytical
stability for observed solitary state, synchronized state, and incoherent
oscillation death state.
