We show theoretically, that the detuning between the stop bands of the two DFB sections gives rise to different self pulsation types: i) dispersive self Q-switching of a single mode (around 10 GHz repetition rate) or ii) beating oscillations between two modes of equal threshold gain (more than 100 GHz). Our analysis is based on the dynamic coupled wave equations, together with carrier rate equations. Using a mode expansion of the optical field, we perform a stability and bifurcation analysis as well as a direct numerical integration of the full equations, which demonstrates the appearence of the two self pulsation types. In the examples investigated, we find finite self pulsation islands in the plane spaned by the two currents, which is in qualitative agreement with published experimental results.