The mean-field dynamics of an array of interacting Bose-Einstein condensates (BECs) is in general non-integrable, and hence it is expected to give rise to strongly irregular, possibly chaotic trajectories. The array consisting of three BECs (trimer) is a paradigm for larger arrays, since it is at the same time sufficiently complex to exhibit a non-integrable mean-field dynamics and sufficiently simple to allow a
thorough analytical study. These features, along with its forthcoming experimental realization, promised by the most recent achievements in the  field of cold atom trapping, make the trimer worth studying.
A description of the mean-field dynamics of the trimer for every choice of the significant Hamiltonian parameters is obtained by means of a systematic analysis of the configuration and stability character of its fixed points. The remarkable operational value of the diagrams summarizing our analytical results is widely confirmed by numerical simulations where slight changes in the parameters give rise to macroscopic (i.e. experimentally accessible) effects.
Furthermore, some preliminary results put into evidence an interesting persistence of mean-field features in the purely quantum description of the system. These investigations are inspired by previous works concerning the symmetric dimer and extend the results reported there to the asymmetric dimer and to the trimer.
A quantum scheme describing the (integrable) dimeric subregime of the trimer dynamics is also proposed. The su(1,1) structure of the relevant quantum Hamiltonian is brought into relation with the stability character of the  dimeric fixed points.