Synchronization in the network-frustrated coupled oscillator with attractive-repulsive frequencies.

We investigate the synchronization behavior of a generalized useful mode of the emergent collective behavior in sets of interacting dynamic elements. The network-frustrated Kuramoto model with interaction-repulsion frequency characteristics is presented, and its structural features are crucial to capture the correct physical behavior, such as describing steady states and phase transitions. Quantifying the effect of small-world phenomena on the global synchronization of the given network, the impact of the random phase-shift and their mutual behavior shows particular challenges.