Intrinsic Localized Modes in Micro-scale Oscillator Arrays Subjected to Deterministic Excitation and White Noise

Abstract

The authors study the influence of noise on an array of micro-scale oscillators with a focus on the phenomenon of intrinsic localized modes (ILMs). It is shown numerically that a white noise excitation, by itself, is unable to produce ILMs. However, under a combined deterministic and random excitation, a noise strength threshold is observed beyond which the ILM at one location in attenuated whilst the localization at another location is strengthened. The results motivate an analytical approach wherein the Fokker-Planck equation and approximate moment evolution equations are derived for a typical cell of the array. Numerical solutions of the moment equations suggest that once a localization event occurs in the array, an excitation with noise strength above a threshold value contributes to the persistence of the event. The reported results can form the basis for developing a fundamental understanding of the influence of noise on ILMs in coupled arrays of nonlinear oscillators including micro-scale oscillator arrays.