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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.
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We der
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by replacing eac
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of a classica
We theoretically study chaos synchronization of two lasers which are delay-coupled via an active or a passive relay. While the lasers are synchronized, their dynamics is identical to a single laser with delayed feedback for a passive relay and identi
We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level.