  Photonic and polaritonic lattices have been recently theoretically proposed
and experimentally realised as many-body simulators due to the rich behaviors
exhibited by such systems at the macroscale. We show that the networks of
polariton condensates encapsulate a large variety of behaviours of systems of
coupled oscillators. By eliminating spatial degrees of freedom in nonresonantly
pumped polariton network, we establish that depending on the values of
experimentally tunable parameters the networks of polariton condensates may
represent Kuramoto, Sakaguchi-Kuramoto, Stuart-Landau, Lang-Kobayashi
oscillators and beyond. The networks of polariton condensates are therefore
capable of implementing various regimes acting as analogue spin Hamiltonian
minimizers, producing complete and cluster synchronization, exotic spin glasses
and large scale secondary synchronization of oscillations. We suggest that the
recently implemented control of the system parameters for individual sites in
polariton lattices allows addressing for the first time the interaction of
sublattices that belong to different oscillatory classes.
