Transition from winnerless competition to synchronization in time-delayed neuronal motifs

The dynamics of brain functional motifs are studied. It is shown that different rhythms can occur in the motifs when time delay is taken into account. These rhythms include synchronization, winnerless competition (WLC) and two plus one (TPO). The main discovery is that the transition from WLC to synchronization can be induced simply by time delay. It is also concluded that some medium time delay is needed to achieve WLC in the realistic case. The motifs composed of heterogeneous neurons are also considered.