  Ensembles of coupled nonlinear oscillators are a popular paradigm and an
ideal benchmark for analyzing complex collective behaviors. The onset of
cluster synchronization is found to be at the core of various technological and
biological processes. The current literature has investigated cluster
synchronization by focusing mostly on the case of attractive coupling among the
oscillators. However, the case of two coexisting competing interactions is of
practical interest due to their relevance in diverse natural settings,
including neuronal networks consisting of excitatory and inhibitory neurons,
the coevolving social model with voters of opposite opinions, ecological plant
communities with both facilitation and competition, to name a few. In the
present article, we investigate the impact of repulsive spanning trees on
cluster formation within a connected network of attractively coupled limit
cycle oscillators. We successfully predict which nodes belong to each cluster
and the emergent frustration of the connected networks independent of the
particular local dynamics at the network nodes. We also determine local
asymptotic stability of the cluster states using an approach based on the
formulation of a master stability function. We additionally validate the
emergence of solitary states and antisynchronization for some specific choices
of spanning trees and networks.
