Rhythmic release of gonadotropin releasing hormone (GnRH) is crucial in the treatment of endocrine disorders related to deficiency in the pulsatile secretion of that hormone. A hydrogel-based hormone delivery system capable of releasing GnRH in a rhythmic, pulsatile manner is being developed. The delivery device functions in the presence of a constant supply of endogenous, glucose and employs a pH-sensitive poly(Aisopropylacrylamide-co-methacrylic acid) [p(NIPA-co-MAA)] hydrogel membrane that exhibits sharp, hysteretic volume phase transitions with changes in pH. pH changes occurring in a chamber bounded by the membrane are caused by conversion of glucose to hydrogen ion catalyzed by glucose oxidase, which decreases pH, and by reaction of H+ with marble (CaCCF), which increases pH. Removal of H+ causes the membrane to swell, thus facilitating transport of glucose and hence production of H+, which causes the membrane to collapse. This negative, nonlinear feedback between the swelling state of the hydrogel membrane and enzymatic conversion of glucose to hydrogen ions results in rhythmic behavior. In this dissertation, issues related to oscillatory and non-oscillatory behavior are investigated. A method is developed to control the heterogeneous kinetics of marble, allowing the “glucose-marble” oscillator to be characterized. Factors affecting sustained periodicity and amplitude of oscillations are identified. Features developed on the hydrogel membrane surface during oscillations are also investigated, and the effect of these morphological changes on oscillator function is discussed.