I/f noise in systems showing stochastic resonance

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 E, 1998

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.

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.

Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), 2018

Physica D: Nonlinear Phenomena, 2003

An array of overdamped bistable oscillators with delay was studied numerically. Each site of the array is coupled directionally with the addition of white Gaussian noise. On the other hand, we compared the results with an array of coupled chain of experimental devices, also fed with Gaussian white noise. We observed for an optimal amount of noise and moderated coupling good transmission along the line without degradation.

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

New Journal of Physics, 2010

Stochastic resonance induced by multiplicative white noise is theoretically studied in forced damped monostable oscillators. A stochastic amplitude equation is derived for the oscillation envelope, which has a linear stochastic resonance. This phenomenon is persistent when nonlinearities are considered. We propose three simple systems-a horizontally driven pendulum, a forced electrical circuit and a laser with an injected signal-that display this stochastic resonance. References 12

2011

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2001

We have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non Gaussian noise. Using a path-integral approach we have obtained a consistent Markovian approximation that enables us to get, through the two state theory, analytical expressions for the signal-to-noise ratio, finding an enhancement of this quantity when the system departs from Gaussian behavior. This finding is supported by extensive numerical simulations.

IEEE Transactions on Instrumentation and Measurement, 2000

Noise-added systems exhibit interesting features in many application fields. In particular, the Stochastic Resonance (SR) phenomenon has been introduced as an innovative approach to understand the behavior and to improve the performance of several classes of systems.

Circuits and Systems …, 1999

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treated.

Physical Review E, 2000

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear-response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input.