Phase drift on networks of coupled crystal oscillators for precision timing

Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. Since the early 1800s, it was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. In modern times, satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network-based model of a high-precision, inexpensive, coupled crystal oscillator system and timing (CCOST) device. A bifurcation analysis (carried out by the authors in a related publication) [Buono et al., SIAM J. Appl. Dyn. Syst. 17, 1310 (2018)1536-004010.1137/16M1066154] of the network dynamics shows a wide variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns. Results from computer simulations seem to indicate that, among all patterns, the standard traveling wave pattern in which consecutive crystals oscillate out of phase by 2π/N, where N is the network size, leads to phase drift error that decreases as 1/N as opposed to 1/sqrt[N] for an uncoupled ensemble. The results should provide guidelines for future experiments, design, and fabrication tasks.