Instability effects in the dynamics of three coupled bosonic wells

We report on the dynamics of three bosonic wells (trimer model) coupled cyclically and occupied by N bosons within the standard mean-field picture. Based on the identification of the fixed points of the dynamics, we find periodic solutions representing the trimer proper modes (the system behavior is discussed for initial conditions close to such states in some relevant cases) and the origin of dynamical instabilities. A diffused chaotic behavior and various macroscopic phenomena are detected numerically. Their dependence on macroscopic model parameters is evaluated as well. Finally, we consider the trimer dynamics for an open chain in the case when the central well has an adjustable depth.