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Photonic and polaritonic lattices have been recently theoretically proposedand experimentally realised as many-body simulators due to the rich behaviorsexhibited by such systems at the macroscale. We show that the networks ofpolariton condensates encapsulate a large variety of behaviours of systems ofcoupled oscillators. By eliminating spatial degrees of freedom in nonresonantlypumped polariton network, we establish that depending on the values ofexperimentally tunable parameters the networks of polariton condensates mayrepresent Kuramoto, Sakaguchi-Kuramoto, Stuart-Landau, Lang-Kobayashioscillators and beyond. The networks of polariton condensates are thereforecapable of implementing various regimes acting as analogue spin Hamiltonianminimizers, producing complete and cluster synchronization, exotic spin glassesand large scale secondary synchronization of oscillations. We suggest that therecently implemented control of the system parameters for individual sites inpolariton lattices allows addressing for the first time the interaction ofsublattices that belong to different oscillatory classes.

Polaritonic network as a paradigm for dynamics of coupled oscillators