M. Franaszek et E. Simiu, STOCHASTIC RESONANCE - A CHAOTIC DYNAMICS APPROACH, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(2), 1996, pp. 1298-1304
For a class of multistable systems it follows from qualitative results
of Melnikov theory that deterministic and stochastic excitations play
equivalent roles in the promotion of chaos. We use such results to su
ggest (1) a method for assessing the role of the noise spectrum in enh
ancing the signal-to-noise ratio (SNR), the most effective spectral sh
ape being that for which the power is distributed closest to the frequ
ency of the Melnikov scale factor's peak; (2) a method for more effect
ive SNR enhancement than can be achieved by increasing the noise, wher
ein the noise is left unchanged and a harmonic excitation with frequen
cy based on the system's Melnikov scale factor is added to the system.
The effectiveness of our Melnikov-based methods is confirmed by numer
ical simulations. The principle of a practical and effective nonlinear
transduction device for enhancing SNR is proposed and demonstrated nu
merically.