Networks of coupled oscillators have been used as models in many biological systems, from neural networks to populations of fireflies. A central question in this area is under what conditions the oscillators will synchronize. In this talk, we initially explore the effect of correlations between the in- and out-degrees (i.e. node-degree correlations) of random directed networks on the synchronization of identical pulse-coupled oscillators. We demonstrate a variety of results through numerical experiments, for example networks with negative node-degree correlation are less likely to achieve global synchrony and synchronize more slowly than networks with positive node-degree correlation. We then show how this effect of node-degree correlation on synchronization of pulse-coupled oscillators is consistent with aspects of network topology (e.g., Laplacian eigenvalues, clustering coefficient) that have been shown to affect synchronization in other contexts. Finally, we end with a more in-depth look into the global dynamics of three oscillators coupled via a directed 3-cycle.
Dynamics of oscillators on random networks
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