Highly accurate precision timing devices are crucial to our modern world. Financial, electric, navigation, and many other systems rely heavily on accurate time measurements for synchronization. Currently, most applications and systems that depend on precision timing work off of the Global Positioning System’s signal. This thesis presents a nonlinear analysis performed on the a of equations that serve as a model for networks of unidirectional coupled Colpitts oscillators. The motivation for these networks lies on their potential to reduce phase drift error through collective behavior. We strive to create an ultra-precision timing system from N numbered Coupled Colpitts Oscillators. This timing device would work independent of the Global Positioning System network and offer robust, accurate timing in environments where devices that rely on the satellite network might fail. We investigate the collective patterns of oscillations that can arise via symmetry breaking bifurcations. By analyzing the symmetry and stability properties of the highly nonlinear governing equations to find phase shift synchronization, we take advantage of the scaling error decrease to achieve better precision timing.
