Forced periodic operation can lead to improved reaction processes. Such operation is studied for the example of the application of a cascade of connected adiabatic fixed-bed reactors to perform catalytic total oxidation. It is shown that the periodic operation of the configuration considered allows an autothermal operation. The concept can outperform classical reverse-flow operation concerning the reduction of slips of unconverted feed. A simple model based on the assumption of a hypothetical countercurrent of the solid phase is derived and compared with a standard dynamical model of the reactor cascade. By evaluation of steady state profiles and application of bifurcation theory, it is demonstrated that the reduced model describes the limiting case for an infinitely segmented cascade and allows assessment of important properties of the periodic process. It permits a fast and detailed analysis of limit point bifurcations, which result in curves enclosing the region of desired ignited states of the reactor. Using singularity analysis further helps to understand the influence of secondary parameters and to identify operational limits.