  Low dimensional dynamics of large networks is the focus of many theoretical
works, but controlled laboratory experiments are comparatively very few. Here,
we discuss experimental observations on a mean-field coupled network of
hundreds of semiconductor lasers, which collectively display effectively
low-dimensional mixed mode oscillations and chaotic spiking typical of
slow-fast systems. We demonstrate that such a reduced dimensionality originates
from the slow-fast nature of the system and of the existence of a critical
manifold of the network where most of the dynamics takes place. Experimental
measurement of the bifurcation parameter for different network sizes
corroborate the theory.
