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An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.

This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadžievski and coworkers. They proposed that a saturable nonlinearity could introduce transition points where localized excitations in nonintegrable lattices would move freely. In our experiments MOS capacitors provide the saturable nonlinearity in an electric lattice. Because of the soft nonlinearity driver locked, auto-resonance stationary ILMs are observed below the bottom of a linear frequency band of the lattice. With decreasing driver frequency the width of the ILM changes in a step-wise manner as does the softening of the barrier between site-centered and bond-centered ILM locations in agreement with theoretical expectations. However, the steps show hysteresis between up and down frequency scans and such hysteresis inhibits the free motion of ILMs.

The speed of a traveling intrinsic localized mode (ILM) in the acoustic spectrum of a micromechanical cantilever array is experimentally measured at high resolution as a function of the driving frequency. A repeating speed pattern is observed for chaotic and regular traveling ILMs between adjacent extended wave normal mode frequencies. The speed of a regular traveling ILM is almost the same as the plane wave dispersion group velocity at that frequency. Since ILM amplification only occurs during reflections at the ends of the array the phase matching condition for long time stability is greatly relaxed. A double humped distribution of speeds, found for chaotic ILMs, is shifted from the regular ILM nearly monochromatic speed value due to the modulational instability. Numerical simulations reproduce many of the experimental observations, demonstrating that intrinsic dynamical properties of the small array are being measured.

Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping a LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum an LSM can be continuously converted into ILMs and visa versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.