THE DYNAMICS OF A CLASS OF COUPLED DIGITAL OSCILLATORS

Coupled first-order digital phase-locked loops (DPLLs), have been prop osed in digital communications and synchronization applications. Previ ously, coupled DPLLs have been studied via extensive computer simulati ons. We obtain dynamics for a generalized class of oscillators, includ ing the DPLLs. The dynamics live on two 'pinched annuli', continuous e verywhere but at the pinches. We prove results concerning the existenc e of all fixed points and period-two points for the general dynamics, briefly discuss the structural stability of these orbits, and then app ly our results to the coupled DPLLs. We also find compelling numerical evidence of a horseshoe (specifically, a subshift of finite-type) in the coupled DPLL dynamics; a proof of this horseshoe is forthcoming.