Comparison of stochastic adaptation and stochastic resonance

Stochastic resonance is a phenomenon possessed by some nonlinear oscillators, in which a weak signal is boosted by noise. Both the monostable and bistable Duffing oscillators can exhibit this property. However, stochastic resonance has a strong frequency-dependence, as only a band of frequencies may be boosted by noise. Adaptive oscillators are a subset of nonlinear oscillators that can learn the features of an external force. Here, an adaptive state is added to a Duffing oscillator. This adaptive state enables the Duffing adaptive oscillator to outperform stochastic resonance over a wide range of frequencies by learning a resonance condition.