Noise-enhanced learning in Duffing adaptive oscillator

Noise typically degrades the performance of physical systems. In some cases, however, noise can provide an enhanced effect. For instance, stochastic resonance may be observed in a nonlinear oscillator when a weak signal is boosted by noise. On the other hand, adaptive oscillators are a type of nonlinear oscillator that can learn and store information in dynamic states. Here, noise is shown to increase the learning rate of an adaptive oscillator, using a Duffing adaptive oscillator. To highlight this effect, stochastic simulations are employed, and the Fokker–Planck equation is semi-analytically solved using the cumulant neglect method. As adaptive oscillators can also be used as a powerful physical reservoir computer architecture, this work shows that the Duffing adaptive oscillator can be optimized for fast learning in noisy environments.