Enhancing detectability of bifurcations in DC-DC converters by stochastic resonance

Noise-driven systems tend to display special features in their power spectra when approaching bifurcation or instability. These features, called noisy precursors, can be of significant use since they can serve as a warning signal for the impending loss of stability. Another phenomenon that has received significant attention in the mathematical physics and biology literature is that of stochastic resonance. In stochastic resonance, the signal-to-noise ratio (SNR) is nonmonotonic with respect to noise level. This cannot occur in linear systems. Most past studies of stochastic resonance involve bistable systems with a weak external periodic forcing. However, recently the same basic phenomenon has been observed in autonomous systems operating along a limit cycle. In any case, the combination of precursors and stochastic resonance provides a tool for instability monitoring. In this paper, these observations are applied to a discrete-time DC-DC converter model. Precursors of period doubling instability are shown to occur. Also, stochastic resonance and its impact on precursor strength is demonstrated. The calculations show how the noise level should be selected to enhance detectability of the impending bifurcation