Stochastic aspects of climatic transitions-response to a periodic
                        forcing

Nicolis, C.

doi:10.3402/tellusa.v34i1.10781

Cited by 153 publications

(106 citation statements)

References 8 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: 55%

“…In this Section we show in considerable detail, both experimentally and theoretically, that phase shifts do indeed accompany SR; however, in continuous systems, they take a form completely different from that predicted for two-state systems (2) . We treat the simplest nontrivial system: an overdamped Brownian particle moving in a symmetric bistable potential and, in addition, driven periodically,…”

Section: Phase Shifts In Stochastic Resonancementioning

confidence: 99%

“…Considered initially in the context of ice-ages (1,2) , it has been observed recently in active (3) and passive (4) optically bistable systems, hybrid electron spin resonance (ESR) devices (5) , a magnetoelastic ribbon (6) , and also in several analogue electronic experiments (7−10) . The origin of SR in all these seemingly different systems lies in the fact that the periodic driving force modulates the probabilities of fluctuational transitions between the co-existing stable states and hence the populations of the states; in its turn this gives rise to a comparatively strong modulation of a coordinate of the system with an amplitude proportional to the distance between the stable positions (11) .…”

Section: Introductionmentioning

confidence: 99%

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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: 55%

Section: Phase Shifts In Stochastic Resonancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic resonance: Linear response and giant nonlinearity

et al. 1993

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“…(ii) Under the simultaneous presence of a stochastic forcing F(t) and a slowly varying periodic forcing, the distribution of probability masses on the two sides of the unstable state may be deeply affected. In particular, the response to the periodic forcing can be substantially enhanced by the noise, a phenomenon referred as stochastic resonance [5]- [7]. (iii) Under the simultaneous presence of a stochastic forcing F(t) and a slow increase of a control parameter in the form of a ramp,…”

mentioning

confidence: 99%

Stochastic resonance in the presence of slowly varying control parameters

Nicolis

2005

New J. Phys.

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Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems

Khovanov

Luchinsky

Mannella

et al.

Modern Nonlinear Optics, Part III

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ii FLUCTUATIONAL ESCAPE AND RELATED PHENOMENA been selected mainly for their own intrinsic scientific interest, but also in order to provide an indication of the power and utility of the simulation approach as a means of focusing on, and reaching an understanding of, the essential physics underlying the phenomena under investigation; they also provide examples of different theoretical approaches and situations where numerical and analogue simulations have led to the development of new experimental techniques and new ideas with potential technological significance. Although the different Sections all share the same general theme -of fluctuational escape phenomena in model nonlinear optical systems -they deal with quite different aspects of the subject; each of them is therefore to a considerable extent self-contained (with Secs. 1.4 and 1.5 being exceptions, because they should be read after Sec. 1.3) and thus can be read almost independently of the others. Before considering particular systems, we review briefly the scientific context of the work and discuss in a general way the significance of escape phenomena in nonlinear optics.The investigation of fluctuations by means of analog or digital simulation is usually found most useful for those systems where the fluctuations of the quantities of immediate physical interest can be assumed to be due to noise. The latter perception of fluctuations goes back to Einstein, Smoluchowski, and Langevin [2, 3, 4] and has often been used in optics (cf. Refs. [5,6,7,8]). In nonlinear optics, the noise can be regarded as arising from two main sources. First there are internal fluctuations in the macroscopic system itself. These arise because spontaneous emission of light by individual atoms occurs at random, and because of fluctuations in the populations of atomic energy levels. The physical characteristics of such noise are usually closely related to the physical characteristics of the model that describes the "regular" dynamics of the system, i.e. in the absence of noise. In particular, the power spectrum of thermal noise and its intensity can be expressed in terms of the dissipation characteristics via the fluctuation-dissipation relations (cf. Ref. [9]) and, if the dissipation is non-retarded so that the corresponding dissipative forces (e.g. the friction force) depend only on the instantaneous values of dynamical variables, the noise power spectrum is independent of frequency, i.e. the noise is white. The model of noise as being white and Gaussian is one of the most commonly used in optics because the quantities of physical interest often vary slowly compared with the fast random processes that give rise to the noise, like emission or absorption of a photon [5,6,7,8]. The second very important source of noise is external: for example, fluctuations of the pump power in a laser. The physical characteristics of such noise naturally vary from one particular system to another; its correlation time is often much longer than that of the internal noise, and its effects can be larg...

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Stochastic aspects of climatic transitions-response to a periodic forcing

Cited by 153 publications

References 8 publications

Stochastic resonance: Linear response and giant nonlinearity

Stochastic resonance: Linear response and giant nonlinearity

Stochastic resonance in the presence of slowly varying control parameters

Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems

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