  We study collective dynamics of interacting centers of exciton-polariton
condensation in presence of spatial inhomogeneity, as modeled by diatomic
active oscillator lattices. The mode formalism is developed and employed to
derive existence and stability criteria of plane wave solutions. It is
demonstrated that $k_0=0$ wave number mode with the binary elementary cell on a
diatomic lattice possesses superior existence and stability properties.
Decreasing net on-site losses (balance of dissipation and pumping) or
conservative nonlinearity favors multistability of modes, while increasing
frequency mismatch between adjacent oscillators detriments it. On the other
hand, spatial inhomogeneity may recover stability of modes at high
nonlinearities. Entering the region where all single-mode solutions are
unstable we discover subsequent transitions between localized quasiperiodic,
chaotic and global chaotic dynamics in the mode space, as nonlinearity
increases. Importantly, the last transition evokes the loss of synchronization.
These effects may determine lasing dynamics of interacting exciton-polariton
condensation centers.
