Synchronisation with non-uniform time-delays (Poster)
I investigate a population of N limit-cycle oscillators coupled on a network structure with time delays introduced by finite signal propagation speed and embedding on a ring. By numerical simulation I find that in complete graphs velocity waves arise that were unknown before. I present attempts to understand these as perturbations of the frequency-locked phase waves which are well-understood. In regular rings and small-world networks frequency synchronisation occurs with a large variety of phase patterns. While all these patterns seem to be almost equally probable in regular rings, small-world topology sometimes prefers one pattern to form for a large number of initial conditions. I propose implications of this for the creation and storage of firing patterns in the context of the temporal coding hypothesis for information processing in the brain. The presented results suggest future analysis in order to improve theoretical understanding of the new phenomena observed and to conclude the work begun here.
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