Dynamics of Coupled Oscillator Systems - Abstract

Pereira, Tiago

Frequency synchronisation induced by large delay

We study how introducing a large delay feedback can induce a synchronisation phenomenon in a neighbourhood of a stable periodic orbit. The synchronisation is made by frequency-locking, which means that any trajectory close to the stable periodic orbit will adjust its rhythm to lock frequency with the delay. We develop a theory of invariant manifold to tackle this problem and discuss applications of these results to networks of lasers.