Network of Coupled Oscillators for Precision Timing

Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. It was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. 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 Oscillator System and Timing device. Preliminary results from computer simulations seem to indicate that timing errors decrease as 1/N when N crystals are coupled as oppose to 1/root N for an uncoupled assemble. This manuscript is aimed, however, at providing a complete classification of the various patterns of collective behavior that are created, mainly, through symmetry-breaking bifurcations. The results should provide guidelines for follow-up simulations, design and fabrication tasks.