The dynamics of the three coupled bosonic wells (trimer) containing N bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as pi-like, dimerlike, and vortex states) representing collective modes are obtained analytically when the fixed points of trimer dynamics are identified on the N=const submanifold in the phase space. Hyperbolic, maximum and minimum points are recognized in the fixed-point set by studying the Hessian signature of the trimer Hamiltonian. The system dynamics in the neighborhood of periodic orbits (associated with fixed points) is studied via numeric integration of trimer motion equations, thus revealing a diffused chaotic behavior (not excluding the presence of regular orbits), macroscopic effects of population inversion, and self-trapping. In particular, the behavior of orbits with initial conditions close to the dimerlike periodic orbits shows how the self-trapping effect of dimerlike integrable subregimes is destroyed by the presence of chaos.