Synchronization phenomena for coupled delay-line oscillators

Abstract

Two coupled delay-line oscillators are modeled by a system of delay differential equations, and their oscillations are analyzed by reducing the delay equations to a system of ordinary differential equations on a finite-dimensional center manifold in the corresponding infinite-dimensional state-space. After averaging the finite-dimensional system, a bifurcation analysis reveals a complex structure of oscillatory behavior. A complete bifurcation analysis is postponed in favor of a bifurcation analysis that is focused on applications to sensor design. In particular, the case of two adjacently mounted, identically built surface acoustic wave (SAW) delay-line oscillators is examined. A bifurcation analysis reveals the operation envelope for a dual SAW sensor based on measurements of frequency differences. The effective operating envelope of this design is limited due to synchronization caused by cross coupling. On the other hand, the operation envelope of a dual SAW sensor can be enlarged by constructing a sensor based on phase differences in the synchronization regime.