Coupled Oscillator Arrays: Dynamics and Influence of Noise
Alofi, Abdulrahman Mohammed
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Coupled oscillator arrays can be used to model several natural systems and engineering systems including mechanical systems. In this dissertation work, the influence of noise on the dynamics of coupled mono-stable oscillators arrays is investigated by using numerical and experimental methods. This work is an extension of recent efforts, including those at the University of Maryland, on the use of noise to alter a nonlinear system's response. A chain of coupled oscillators is of interest for this work. This dissertation research is guided by the following questions: i) how can noise be used to create or quench spatial energy localization in a system of coupled, nonlinear oscillators? and ii) how can noise be used to move the energy localization from one oscillator to another? The coupled oscillator systems of interest were harmonically excited and found experimentally and numerically to have a multi-stability region (MR) in the respective frequency response curves. Relative to this region, it has been found that the influence of noise depends highly on the excitation frequency location in the MR. Near either end of the MR, the oscillator responses were found to be sensitive to noise addition in the input and it was observed that the change in system dynamics through movement amongst the stable branches in the deterministic system could be anticipated from the corresponding frequency response curves. The system response is found to be robust to the influence of noise as the excitation frequency is shifted toward the middle of the MR. Also, the effects of noise on different response modes of the coupled oscillators arrays were investigated. A method for predicting the behavior is based on so-called basins of attractions of high dimensional systems. Through the findings of this work, many unique noise influenced phenomena are found, including spatial movement of an energy localization to a neighboring oscillator, response movement gradually up the energy branches, and generation of energy cascades from a localized mode.