  A class of adaptation functions is found for which a synchronous oscillation
mode exists in the network of phase oscillators with triadic couplings. It is
shown that the destruction of the synchronous mode occurs differently for
networks with pairwise couplings and with higher-order interactions. In the
first case, a chimera state is realized. In the second case, the destruction of
the synchronous state occurs more abruptly, and the chimera state is not
formed. The patterns of formation of synchronization and desynchronization
modes are determined.
