Theory of stochastic resonance

McNamara, Bruce; Wiesenfeld, Kurt

doi:10.1103/physreva.39.4854

Cited by 1,495 publications

(977 citation statements)

References 14 publications

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“…The first prediction of a phase shift seems to have been due to Nicolis (2) who concluded that, for an overdamped system fluctuating in a bistable potential, φ = −arctan(Ω/W (0) ) where W (0) is the sum of the transition rates out of each of the potential wells; similar results were also obtained by McNamara and Wiesenfeld (12) . On the other hand, Gammaitoni et al, claimed (9) that analog simulations (10) as well as numerical computations (15) "had ruled out [the phase shifts] as apparently spurious".…”

Section: Phase Shifts In Stochastic Resonancesupporting

confidence: 67%

“…Overall, it follows from (12), (13) (see also Fig. 2 where φ vs D as given by (12) is plotted) that the phase shift displays a resonance-type (nonmonotonic) behaviour as a function of the noise intensity D. This prediction is in contrast with the earlier theories (2,12) for two-state systems displaying SR in the signal-to-noise ratio, but exhibiting a monotonic dependence of |φ| on D; the phase shift in these theories is described by Eq. (13) with Ω r set equal to ∞ (if the intrawell relaxation was infinitely fast the intrawell motion would not come into play and the system would behave as a two-state one):…”

Section: Phase Shifts In Stochastic Resonancecontrasting

confidence: 54%

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Stochastic resonance: Linear response and giant nonlinearity

et al. 1993

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The response of a bistable noise-driven system to a weak periodic force is investigated using linear response theory (LRT) and by analogue electronic experiment. For quasi-thermal systems the response, and in particular its increase with increasing noise intensity D, are described by the fluctuation-dissipation relations. For small D the low-frequency susceptibility of the system χ(ω) has been found in explicit form allowing for both forced oscillations about the stable states and periodic modulation of the probabilities of fluctuational transitions between the states. It is shown, both theoretically and experimentally, that a phase lag φ between the force and the response passes through a maximum when D is tuned through the range where stochastic resonance (SR) occurs. A giant nonlinearity of the response is shown to arise for small D and small frequencies of the driving force. It results in the signal induced by a sinusoidal force being nearly rectangular. The range of applicability of LRT is established.

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Section: Phase Shifts In Stochastic Resonancesupporting

confidence: 67%

Section: Phase Shifts In Stochastic Resonancecontrasting

confidence: 54%

Stochastic resonance: Linear response and giant nonlinearity

et al. 1993

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“…Such an effect is seen when the response of a system to a drive depends non-monotonically on noise, with an optimum at a moderate, non-zero, noise level. There are many pointers in the literature to physical evidences of stochastic resonance in physical systems [69,11,23,24,47,71,70], and in models of neurons [8,42,55,54]. In living systems stochastic resonance has been reported in crayfish mechanoreceptors [16], the cricket cercal sensory system [40], neural slices [27], hippocampus [72], and the cortex [48].…”

Section: A Relation To Stochastic Resonance: Model Bmentioning

confidence: 99%

Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocorrelation

Mayor

Gerstner

2004

Journal of Physiology-Paris

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We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes.We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation of the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.

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“…The idea of approximation of diffusions in potential landscapes by appropriate finite state Markov chains in the context of stochastic resonance was suggested by Eckmann and Thomas [6], and C. Nicolis [15], and developed by McNamara and Wiesenfeld [14]. In this section we follow [17,13].…”

Section: The 'Effective Dynamics': Two-state Markov Chainmentioning

confidence: 99%

Stochastic Resonance: A Comparative Study of Two-State Models

Imkeller

Pavlyukevich

2004

Seminar on Stochastic Analysis, Random Fields and Applications IV

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Abstract. We consider a dynamical system describing the motion of a particle in a double well potential with a periodic perturbation of very small frequency, and an additive stochastic perturbation of amplitude ε. It is in stochastic resonance if the solution trajectories amplify the small periodic perturbation in a 'best possible way'. Systems of this type first appeared in simple energy balance models designed for a qualitative explanation of global glacial cycles. Large deviations theory provides a lower bound for the proportion of the amplitude and the logarithm of the period above which quasi-deterministic periodic behavior can be observed. However, to obtain optimality, one has to measure periodicity with a measure of quality of tuning such as spectral power amplification favored in the physical literature. In a situation where the potential switches discontinuously between two spatially antisymmetric double well states we encounter a surprise. Contrary to physical intuition, the stochastic resonance pattern is not correctly given by the reduced dynamics described by a two state Markov chain with periodic hopping rates between the potential minima which mimic the large (spatial) scale motion of the diffusion. Only if small scale fluctuations inside the potential wells where the diffusion spends most of its time are carefully eliminated, the Markov chain gives the correct picture.

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Theory of stochastic resonance

Cited by 1,495 publications

References 14 publications

Stochastic resonance: Linear response and giant nonlinearity

Stochastic resonance: Linear response and giant nonlinearity

Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocorrelation

Stochastic Resonance: A Comparative Study of Two-State Models

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