Adaptation rules inducing synchronization of heterogeneous Kuramoto oscillator network with triadic couplings

Abstract: 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.