  The global attraction is established for all finite energy solutions to a
model $\mathbf{U}(1)$-invariant nonlinear Klein-Gordon equation in one
dimension coupled to a finite number of nonlinear oscillators: We prove that
{\it each finite energy solution} converges as $t\to\pm\infty$ to the set of
all ``nonlinear eigenfunctions'' of the form $\phi(x)e\sp{-i\omega t}$ if all
oscillators are strictly nonlinear, and the distances between all neighboring
oscillators are sufficiently small. The {\it global attraction} is caused by
the nonlinear energy transfer from lower harmonics to the continuous spectrum
and subsequent dispersive radiation. This result for one oscillator was
obtained in [KK07].
  We construct counterexamples showing that the convergence to the solitary
waves may break down if the distance between some of the neighboring
oscillators is sufficiently large or if some of the oscillators are harmonic.
In these cases, the global attractor can contain ``multifrequency solitary
waves'' or linear combinations of distinct solitary waves.
