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Stochastic Resonance; A Chaotic Dynamics Approach.

pdf icon Stochastic Resonance; A Chaotic Dynamics Approach. (569 K)
Franaszek, M.; Simiu, E.

Physical Review E, Vol. 54, No. 2, 1298-1304, August 1996.


chaos; noise (sound)


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 suggest: (1) a method for assessing the role of the noise spectrum in enhancing the signal-to-noise ratio (SNR), the most effective spectral shape being that for which the power is distributed closest to the frequency of the Melnikov scale factor's peak; (2) a method for more effective SNR enhancement than can be achieved by increasing the noise, wherein the noise is left unchanged and a harmonic excitation with frequency based on the system's Melnikov scale factor is added to the system. The effectiveness of our Melnikov-based methods is confirmed by numerical simulations. The principle of a practical and effective nonlinear transduction device for enhancing SNR is proposed and demonstrated numerically.