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We present the phase diagram of the mean-field driven-dissipative Bose–Hubbard dimer model. For a dimer with repulsive on-site interactions ( U  > 0) and coherent driving, we prove that ${{\mathbb{Z}}}_{2}$ -symmetry breaking, via pitchfork bifurcations with sizable extensions of the asymmetric solutions, require a negative tunneling parameter ( J  < 0). In addition, we show that the model exhibits deterministic dissipative chaos. The chaotic attractor emerges from a Shilnikov mechanism of a periodic orbit born in a Hopf bifurcation and, depending on its symmetry properties, it is either localized or not.