A. James Clark School of Engineering
Permanent URI for this communityhttp://hdl.handle.net/1903/1654
The collections in this community comprise faculty research works, as well as graduate theses and dissertations.
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Item Coupled Oscillator Arrays: Dynamics and Influence of Noise(2021) Alofi, Abdulrahman Mohammed; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)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.Item The Effects of Coupling Delay and Amplitude / Phase Interaction on Large Coupled Oscillator Networks(2012) Lee, Wai Shing; Ott, Edward; Antonsen, Thomas M.; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The interaction of many coupled dynamical units is a theme across many scientific disciplines. A useful framework for beginning to understanding such phenomena is the coupled oscillator network description. In this dissertation, we study a few problems related to this. The first part of the dissertation studies generic effects of heterogeneous interaction delays on the dynamics of large systems of coupled oscillators. Here, we modify the Kuramoto model (phase oscillator model) to incorporate a distribution of interaction delays. Corresponding to the continuum limit, we focus on the reduced dynamics on an invariant manifold of the original system, and derive governing equations for the system, which we use to study stability of the incoherent state and the dynamical transitional behavior from stable incoherent states to stable coherent states. We find that spread in the distribution function of delays can greatly alter the system dynamics. The second part of this dissertation is a sequel to the first part. Here, we consider systems of many spatially distributed phase oscillators that interact with their neighbors, and each oscillator can have a different natural frequency, and a different response time to the signals it receives from other oscillators in its neighborhood. By first reducing the microscopic dynamics to a macroscopic partial-differential-equation description, we then numerically find that finite oscillator response time leads to many interesting spatio-temporal dynamical behaviors, and we study interactions and evolutionary behaviors of these spatio-temporal patterns. The last part of this dissertation addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics. Our first goal is to investigate the effect of a spread in the amplitude growth parameter of the oscillators and that of a homogeneous nonlinear frequency shift. Both of these effects are of potential relevance to recently reported experiments. Our second goal is to gain further understanding of the observation that, at large coupling strength, a simple constant-amplitude sinusoidal oscillation is always a solution for the dynamics of the global order parameter when the system has constant nonlinear characteristics.