Comparison of aperiodic stochastic resonance in a bistable system realized by adding noise and by tuning system parameters

Abstract

Two methods of realizing aperiodic stochastic resonance (ASR) by adding noise and tuning system parameters in a bistable system, after a scale transformation, can be compared in a real parameter space. In this space, the resonance point of ASR via adding noise denotes the extremum of a line segment, whereas the method of tuning system parameters presents the extrema of a parameter plane. We demonstrate that, in terms of the system performance, the method of tuning system parameters takes the precedence of the approach of adding noise for an adjustable bistable system. Besides, adding noise can be viewed as a specific case of tuning system parameters. Further research shows that the optimal system found by tuning system parameters may be subthreshold or suprathreshold, and the conventional ASR effects might not occur in some suprathreshold optimal systems.

Noise benefits in joint detection and estimation problems

“…The constraints are selected as the probabilities of false alarm and detection of the original system without any additive noise, which correspond to Rð0Þ and Tð0Þ, respectively (see (9) and (10)). In other words, while minimizing the conditional estimation risk, no degradation is allowed in the detection part of the system.…”

“…In the field of statistical signal processing, noise benefits are investigated in various studies such as [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In [2], it is shown that the detection probability of the optimal detector for a described network with nonlinear elements driven by a weak sinusoidal signal in white Gaussian noise is non-monotonic with respect to the noise power and fixed false alarm probability; hence, detection probability enhancements can be achieved via increasing the noise level in certain scenarios.…”

“…One approach for realizing noise benefits is to tune the parameters of a nonlinear system, as employed, e.g., in [8][9][10][11][12]. An alternative approach is the injection of a random process independent of both the meaningful information signal (transmitted or hidden signal) and the background noise (undesired signal).…”

Enhancement of stochastic resonance by tuning system parameters and adding noise simultaneously

“…Obviously, A should take the maximal value in order to paper [17] shows that the noise intensity cannot be adjusted maximize SNR. From (4), this means that the noise and must be fixed at the initial value (no noise will be intensity should be fixed to its initial value Do which is also added) in order to minimize the bit error rate (BER) for the the minimal noise intensity, assuming the signal amplitude aperiodic stochastic resonance (ASR).…”

Enhancement of Stochastic Resonance Using Optimization Theory

“…This is called parameter-tuning stochastic resonance [17] [23]. It is also shown that tuning system parameters is a better method in some situations than adding noise, especially when the initial noise intensity is already beyond the resonance region [18]. Among this research, either noise is added, or the system parameters are tuned, but not both.…”