UC Santa Barbara

Precise synchronization among networked agents is responsible for phenomena as diverse as coral spawning and consistency in stock market transactions. The importance of synchronization in biological and engineering systems has triggered an avalanche of studies analyzing the emergence of a synchronized behavior within a network of, possibly heterogeneous, agents. In particular, synchronization of networks of coupled oscillators has received great attention since limit cycle oscillators are a natural abstraction for systems where periodicity is a distinctive property. Examples of such systems include circadian rhythms and alternate-current power generators. This work deals with synchronization of pulse-coupled limit cycle oscillators (PCOs). A reverse engineering approach is taken with the objective of obtaining an abstraction for PCO networks able to capture the key properties observed in the classical biological PCO model, to finally implement it in an en gineering system. To this end, we first reformulate the PCO model as a hybrid system, able to integrate in a smooth manner the continuous-time dynamics of the individual oscillators and the impulsive effect of the coupling. Using our new model, we analyze the existence and stability of synchronization in a variety of PCO network topologies, starting from the simplest all-to-all network where global synchronization is proven to exist, to end giving synchronization conditions in the general strongly connected network case. Inspired by the strong synchronization properties of PCO networks we design a PCO-inspired time synchronization protocol for wireless sensor networks that enjoys all the advantages of our optimized PCO setup. A pilot implementation is presented going from a simulation stage to a hardware implementation in Gumstix development boards and industrial acoustic sensors. To test the potential of the protocol in a real application, we implement the PCO-based time synchronization protocol in a distributed acoustic event detection system, where a sensor network combines local measurements over an infrastructure-free wireless network to find the source of an acoustic event. An evaluation by simulation is given to illustrate the advantages of using the pulse-coupled synchronization strategy.

The contributions of this thesis range from the theoretical synchronization conditions for a variety of PCO networks to the design and implementation of a synchronization strategy for wireless sensor networks that seems to be the natural choice when using an infrastructure-free wireless network due to its simple formulation and natural scalability.