High frequency stochastic resonance in periodically driven systems (original) (raw)

Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems

The European Physical Journal B, 1998

A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily.

Nonconventional stochastic resonance

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.

Stochastic resonance in bistable systems driven by harmonic noise

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

Stochastic resonance in a mono-stable system subject to frequency mixing periodic force and noise

The phenomenon of stochastic resonance (SR) in a biased mono-stable system driven by multiplicative and additive white noise and two periodic fields is investigated. Analytic expressions of the signal-to-noise ratio (SNR) for fundamental harmonics and higher harmonics are derived by using the two-state theory. It is shown that the SNR is a non-monotonic function of the intensities of the multiplicative and additive noises, as well as the bias of the mono-stable system and SR appears at both fundamental harmonics and higher harmonics. Moreover, the higher the order of mixed harmonics is, the smaller the SNR values are, that is, the suppression exists for higher harmonics.

Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime

Physica D: Nonlinear Phenomena, 2006

We present results of an experimental study of stochastic resonance in an electronic Chua's circuit whose dynamics switches between two different stable chaotic attractors when it is driven by a periodic signal and a Gaussian white noise. Due to the internal dynamics of the attractors the minimum amplitude for the external forcing to induce jumps strongly depends on the external frequency. We determine from the Fourier transform of the output signal the amplification factor of the input signal and study its dependence on the external frequency and the noise intensity. We show that the envelope of the distribution of switching times follows a gamma distribution, typical from bistable systems, and that the mean switching time decays exponentially with the noise intensity. We propose a simple method for obtaining the optimal noise intensity from the residence and switching times probability distributions and show that it coincides with the value obtained from the maximum of the amplification factor. (C.R. Mirasso). resonance in deterministic dynamical systems and, since it is induced by the noise, it is called stochastic resonance. The study of stochastic resonance in bistable systems has also been extended to excitable systems having a single rest state and to threshold detectors (a pulse occurs whenever the sum of the signal and the noise at the input crosses a threshold). Since the conditions for the appearance of stochastic resonance do not depend on very specific model details, it has been observed in many different fields such as paleoclimatology, lasers, neurophysiology, electronic detectors, etc. and studies of this phenomenon cross disciplinary boundaries. Various reviews [1-4] address the recent and extensive work on this fascinating subject.

The mechanism of stochastic resonance

Journal of Physics A: Mathematical and General, 1981

It is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance (peak in the power spectrum) which is absent when either the forcing or the perturbation is absent.

Stochastic resonance in periodic potentials

Physical Review E, 2011

The phenomenon of stochastic resonance (SR) is known to occur mostly in bistable systems. However, the question of the occurrence of SR in periodic potential systems has not been resolved conclusively. Our present numerical work shows that the periodic potential system indeed exhibits SR in the high-frequency regime, where the linear-response theory yields maximum frequency-dependent mobility as a function of noise strength. The existence of two (and only two) distinct dynamical states of trajectories in this moderately feebly damped periodically driven noisy periodic potential system plays an important role in the occurrence of SR.

A new perspective on stochastic resonance in monostable systems

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

Periodically time-modulated bistable systems: Stochastic resonance

Physical Review A, 1989

We characterize the notion of stochastic resonance for a wide class of bistable systems driven by a periodic modulation. On developing an adiabatic picture of the underlying relaxation mechanism, we show that the intensity of the effect under study is proportional to the escape rate in the absence of perturbation. The adiabatic model of stochastic resonance accounts for the role of Anite damping and finite noise correlation time as well. Our predictions compare well with the results of analogue simulation.