Rhythmic neural activity is thought to underlie many high-level functions of the nervous system. Our goals are to understand rhythmic activity starting with small networks, using theoretical and experimental tools. Phase resetting theory describes essential properties that cause and destroy rhythms. We validate and extend one branch of this theory, testing it in bursting neurons coupled by excitation and then extending the theory to account for temporal variability found in our experimental data. We show that the theory makes good predictions of rhythmic activity in heterogeneous networks. We also note differences in mathematical structure between inhibition- and excitation-coupling that cause them to behave differently in noisy contexts and may explain why all central pattern generators (CPGs) found in nature are dominated by inhibition. Our extension of the theory gives a method that is useful to compare experimental and model data and shows that noise may either create or destroy a rhythm. Finally, we described the cellular mechanisms in Aplysia that switch the feeding CPG from arrhythmic to rhythmic behavior in response to reward stimuli. Previous studies showed that a Dopamine reward signal is correlated to changes in electrical coupling and excitability in several important neurons in the CPG. Using the dynamic clamp and an in vitro analog of the full behavioral system, we were able to determine that electrical coupling alone controls rhythmicity, while excitability independently controls the rate of activity. These results beg for further study, including new theory to explain them fully.