Precise time is crucial to a variety of economic activities around the world. Communication systems, electrical power grids, and financial networks all rely on precision timing for synchronization and operational efficiency. The free availability of GPS time has enabled cost savings for industrial and scientific developments that depend on precise time and has led to significant advances in capability. For example, wireless telephone and data networks use GPS time to keep all of their base stations in perfect synchronization. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this critical need, we investigated in previous work the collective patterns of oscillations that can arise, via symmetry-breaking bifurcations, in networks of coupled nonlinear oscillators with the goal of reducing phase drift via collective responses. In that work the emphasis was purely on the existence and stability properties of collective patterns of oscillations. In this thesis, we investigate the effects of noise on phase drift with the additional goal of determining which patterns of oscillations can lead to the optimal phase error reduction and, ultimately, to improve precision timing. The underlying objective is to design and fabricate a high-precision, inexpensive, Coupled Crystal Oscillator System and Timing (CCOST) with a scaling error of 1/N, that can operate when GPS service degrades or is denied.
