Abstract
An analogy between crowd synchrony and multi-layer neural network architectures is proposed. It indicates that many non-identical dynamical elements (oscillators) communicating indirectly via a few mediators (hubs) can synchronize when the number of delayed couplings to the hubs or the strength of the couplings is large enough. This phenomenon is modeled using a system of semiconductor lasers optically delay-coupled in either a fully connected or a diluted manner to a fixed number of non-identical central hub lasers. A universal phase transition to crowd synchrony with hysteresis is observed, where the time to achieve synchronization diverges near the critical coupling independent of the number of hubs.
Highlights
The first is whether the emergence of crowd synchrony is a phase transition when the number and strength of the couplings is increased and if so whether the transition is continuous or discontinuous
The hidden units (HUs) lasers as well as the lasers in the lower layer are all assumed to have pump currents well below pth, and in the simulations we investigate a range of injection currents for the lower/upper layers
We find that crowd synchrony can emerge in a diluted system where the lower layer lasers are influenced by different subsets of HUs
Summary
The first is whether the emergence of crowd synchrony is a phase transition when the number and strength of the couplings is increased and if so whether the transition is continuous or discontinuous. The time needed to achieve crowd synchrony for a given architecture diverges as the coupling strength approaches c from above.
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