  We describe the emergence and interactions of breather modes and resonant
wave modes within a two-dimensional ring-like oscillator chain in a
microcanonical situation. Our analytical results identify different dynamical
regimes characterized by the potential dominance of either type of mode. The
chain is initially placed in a meta-stable state which it can leave by passing
over the brim of the applied Mexican-hat-like potential. We elucidate the
influence of the different wave modes on the mean-first passage time. A central
finding is that also in this complex potential landscape a fast noise-free
escape scenario solely relying on nonlinear cooperative effects is
accomplishable even in a low energy setting.
