I/f noise in systems showing stochastic resonance

TEM Journal

This paper investigates the stochastic resonance in nonlinear system driven by an additive signal-noise mixture. No exact analytical solution of the stochastic resonance equation has been found. It is usually solved approximately. In this paper, this equation is solved numerically. The noise dispersion under the stochastic resonance effect is determined. This study has convincingly shown that a weak signal could be amplified due to noise power and the output signal-to-noise ratio has a nonlinear dependence on the noise level. The results are applicable to radars in telecommunications and radio engineering.

Physical Review Letters, 1998

We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a wide class of non-dynamical systems, covering situations of different nature. Some particular examples are discussed in detail.

Reviews of Modern Physics, 1998

Circuits and Systems …, 1999

Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory.

Physical Review Letters, 2002

In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non Gaussian noise. In agreement with the theoretical predictions our main findings are: an enhancement of the sensibility of the system together with a remarkable widening of the response (robustness). This implies that even a single resonant unit can reach a marked reduction in the need of noise tuning.

Journal of Statistical Physics, 1993

It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.

2003

We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise.

Physics-Uspekhi, 1999

Stochastic resonance (SR) provides a glaring example of a noise-induced transition in a nonlinear system driven by an information signal and noise simultaneously. In the regime of SR some characteristics of the information signal (amplification factor, signal-to-noise ratio, the degrees of coherence and of order, etc.) at the output of the system are significantly improved at a certain optimal noise level. SR is realized only in nonlinear systems for which a noise-intensity-controlled characteristic time becomes available. In the present review the physical mechanism and methods of theoretical description of SR are briefly discussed. SR features determined by the structure of the information signal, noise statistics and properties of particular systems with SR are studied. A nontrivial phenomenon of stochastic synchronization defined as locking of the instantaneous phase and switching frequency of a bistable system by external periodic force is analyzed in detail. Stochastic synchronization is explored in single and coupled bistable oscillators, including ensembles. The effects of SR and stochastic synchronization of ensembles of stochastic resonators are studied both with and without coupling between the elements. SR is considered in dynamical and nondynamical (threshold) systems. The SR effect is analyzed from the viewpoint of information and entropy characteristics of the signal, which determine the degree of order or self-organization in the system. Applications of the SR concept to explaining the results of a series of biological experiments are discussed. 7. Stochastic synchronization as noise-enhanced order 28 7.1 Dynamical entropy and source entropy in the regime of stochastic synchronization; 7.2 Stochastic resonance and Kullback entropy; 7.3 Enhancement of the degree of order in an ensemble of stochastic oscillators in the SR regime 8. Stochastic resonance and biological information processing 31 8.1 Stochastic resonance in the mechanoreceptors of the crayfish; 8.2 The photoreceptor system of the crayfish; 8.3 SR as a tool for quantifying human visual processes 9. Conclusions 33 References 34

Jetp Letters, 1993

High frequency stochastic resonance (SR) phenomena, associated with fluctuational transitions between coexisting periodic attractors, have been investigated experimentally in an electronic model of a single-well Duffing oscillator bistable in a nearly resonant field of frequency $\omega_F$. It is shown that, with increasing noise intensity, the signal/noise ratio (SNR) for a signal due to a weak trial force of frequency $\Omega \sim \omega_F$ at first decreases, then {\it increases}, and finally decreases again at higher noise intensities: behaviour similar to that observed previously for conventional (low frequency) SR in systems with static bistable potentials. The stochastic enhancement of the SNR of an additional signal at the mirror-reflected frequency $\vert \Omega - 2 \omega_F \vert$ is also observed, in accordance with theoretical predictions. Relationships with phenomena in nonlinear optics are discussed.

Physical review letters, 1994

We study stochastic resonance in a bistable system which is excited simultaneously by white and harmonic noise which we understand as the signal. In our case the spectral line of the signal has a nite width as it occurs in many real situations. Using techniques of cumulant analysis as well as computer simulations we nd that the e ect of stochastic resonance is preserved in the case of harmonic noise excitation. Moreover we show that the width of the spectral line of the signal at the output can be decreased via stochastic resonace. The last could be of importance in the practical using of the stochastic resonance. PACS number(s): 05.40.+j, 02.50.+s Typeset using REVT E X