Energy dissipation threshold and self-induced transparency in systems with discrete breathers

The energy propagation through a chain of coupled anharmonic oscillators under the influence of a harmonic driving force applied at one end is numerically investigated using the nonlinear response manifold method and real time simulations. For driving frequencies in the band gap of the linear spectrum, where energy propagation is impossible in linear systems, the existence of propagation thresholds for the amplitude of the driving force is related to the existence of turning points in the nonlinear response manifold and can be associated with discrete breathers at the driving frequency. A rich dynamical behavior involving several mechanisms of nonlinear transmission is exhibited that depends to a great extent on the local response of the forced nonlinear oscillator at the edge of the system. At low force amplitudes, a localized quasilinear response of this first site blocks energy propagation. Above a certain amplitude threshold, which is determined by the stability of the mode localized on the first site, the chain exhibits dissipative response and weak propagation occurs through linear modes of the system. Increasing further the driving amplitude, this phonon radiation remains the only propagation process, up to a second threshold amplitude at which energy transmission dramatically increases by a few orders of magnitude. This large energy flow is due to large amplitude nonlinear waves which in some cases appear as mobile discrete breathers propagating throughout the chain.