Bacterial quorum-sensing systems have been used for the construction of artificial genetic networks with complex spatial and temporal behaviors. The complexities of these artificial systems are derived from the properties of the quorum-sensing system components, which determine cellular responses depending on the synthesis and detection of an intracellular signaling molecule or peptide. Using components isolated from the LuxI-LuxR system originally identified in the marine bacterium Vibrio fischeri, we have constructed a simple genetic circuit incorporating positive feedback. The characteristics of the circuit were examined through dynamic studies done at the population level, and steady-state single-cell measurements. The effects of different component properties on the network were also probed using mutants of the LuxR transcriptional activator with increased or decreased activities. Development of a stochastic model based on these results allowed for further inspection of component properties, and an analysis of noise present in the network.