The changes in behavior that lead to a period-doubling bifurcation were investigated in the application of cyclic voltammetry to the oxidation of methanol at a rotating platinum disk electrode in alkaline solution. Two parameters were separately varied, the concentration of methanol and the upper potential limit of the potential cycle. Feedback mechanisms that explain the changes in behavior are formulated from experimental data and an electrochemical mechanism. Evidence is presented that indicates a period-two cyclic voltammogram occurs due to the dual role played by the surface species PtOH. During one cycle of the period-two response, most of the PtOH that forms on the surface reacts with an intermediate of methanol oxidation. During the other cycle a substantial amount of PtOH is transformed to Pt oxides. A Mobius strip that formed before the period-doubling bifurcation was detected by examining current-potential curves. Near the point in parameter space where the Mobius strip formed the relaxation was fastest.