I used nonlinear analysis to model a Wein Bridge oscillator circuit, both fully linear and stabilized with a incandescent lightbulb. In the fully linear case, I modelled the saturation of the operational amplifier, which demonstrates a degenerate Hopf bifurcation. For the lightbulb, I developed a differential equation to model the radiative heat transfer and temperature of the lightbulb filament, and ultimately the resistance. Based on this analysis and experimental characterization of the lightbulb, I specified component values to create stable oscillations that accurately matched my model.