This paper approaches DC-DC power converters topologically and statistically. The approach is able to analyze simultaneously periodic and aperiodic behavior. Local c-bifurcation and qualitative analysis are performed on boost converters. The golden mean's importance is highlighted. An analytical expression for the inductor current ripple is derived using statistical analysis. Switching losses during aperiodic operation are compared with periodic ones. Possible applications for an aperiodic DC-DC power converter are suggested.