  Long-range interacting systems are omnipresent in nature. We investigate here
the collective dynamical behavior in a long-range interacting system consisting
of coupled Stuart-Landau limit cycle oscillators. In particular, we analyze the
impact of a repulsive coupling along with symmetry breaking coupling. We report
that the addition of repulsive coupling of sufficient strength can induce a
swing of the synchronized state which will start disappearing with an
increasing disorder as a function of the repulsive coupling. We also deduce
analytical stability conditions for the oscillatory states including
synchronized state, solitary state, two-cluster state as well as oscillation
death state. Finally, we have also analyzed the effect of power-law exponent on
the observed dynamical states.
