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Dynamics and Bifurcations in Coupled Bistable Systems with Applications to Engineering Devices
Lyons, Daniel Carl
Palacios, AntonioMahaffy, JosephNadim, AliAngus, JohnCarretero, Ricardo
xvi, 261 pages : illustrations
Bistability is a highly prevalent phenomenon that occurs in a variety of natural and artificial settings. For example, it is used in the human body for the regulation of the cell cycle, and in electronics, it is used to engineer Schmitt trigger circuits. Bistable systems possess a mechanism that allows them to switch between two stable states when an energy threshold is exceeded. Recent work demonstrates that coupled bistable systems may be designed to exploit coupling-induced oscillations to obtain some desirable property. The generic properties of coupled bistable systems are investigated via case studies of a Coupled Core Fluxgate Magnetometer and a Nonlinear Channelizer. With the stable manifold theorem and suitable numerical methods, the basins of attraction and their evolution upon changes of parameters are studied in the undriven case. It is shown theoretically that an N-element coupled bistable array driven by a periodic signal with frequency f may produce a traveling wave pattern if the frequency of the array of oscillators is f/(kN), where k is an integer. Computational work confirms this theoretical finding, and many frequency-locking regions of large size are found. An algorithm is described for the demodulation of phase-modulated signals by a coupled bistable system, and the performance of the algorithm is studied in the presence of device noise. The effects of a constant coupling time delay are also investigated computationally for coupled bistable arrays. Overall, coupled bistable systems are shown to exhibit many generic properties that may be exploited for the design of novel future technologies.
Includes bibliographical references (pages 244-261).
Doctor of Philosophy (Ph.D.) Claremont Graduate University and San Diego State University, 2014
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