Cyclic motifs as the governing topological factor in time-delayed oscillator networks

Abstract

We identify the relative amount of short cyclic motifs as an important topological factor in networks of time delayed Kuramoto oscillators. The patterns emerging from the cyclic motifs are most clearly distinguishable in the average frequency and the momentary frequency dispersion as a function of the time delay. In particular, the common distinction between bi-directional and unidirectional couplings is shown to have a decisive effect on the network dynamics. We argue that the behavior peculiar to the sparsely connected uni-directional random network can be described essentially as the lack of distinguishable patterns originating from cyclic motifs of any specific length.