Nonlinear saturation of prebifurcation noise amplification

Kravtsov, Yu. A.; Surovyatkina, Elena

doi:10.1016/j.physleta.2003.10.034

Cited by 26 publications

(19 citation statements)

References 8 publications

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“…The estimates presented above, are in good agreement with the results of numerical simulation, performed in (Kravtsov and Surovyatkina, 2003) and shown by a continuous line at Fig. 1.…”

Section: Prebifurcation Noise Amplification At the Threshold Of Periosupporting

confidence: 86%

“…This is true not only for period-doubling bifurcations (Kravtsov and Surovyatkina, 2003), but also for pitchfork bifurcations.…”

Section: On Weak Noise Measurements On Basis Of Nonlinear Saturation mentioning

confidence: 86%

“…According to (Wiesenfeld, 1987), prebifurcation noise amplification might be an effective diagnostic instrument for nonlinear systems (so named "noisy precursor" of bifurcation), see also (Wiesenfeld, 1985). Nonlinear saturation of fluctuations in the vicinCorrespondence to: E. Surovyatkina (selena@iki.rssi.ru) ity of bifurcation point was studied in the papers (Kravtsov and Surovyatkina, 2001;Kravtsov et al, 2003) for the case of sufficiently slow (quasi-stationary) bifurcation. In this paper we shall show, that rapid bifurcation transitions cause decreasing of the noise amplification.…”

Section: Introductionmentioning

confidence: 99%

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Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems

Surovyatkina

2005

Nonlin. Processes Geophys.

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Abstract. The phenomena of prebifurcation noise amplification and noise-dependent hysteresis are studied as prospective indicators of bifurcations ("noisy precursor") in nonlinear Geophysical systems. The phenomenon of prebifurcation noise amplification arises due to decreasing of damping coefficients just before bifurcation. A simple method for the estimation of the forced fluctuation variance is suggested which is based on results of linear theory up to the boundary of its validity. The upper level for the fluctuation variance before the onset of the bifurcation is estimated from the condition that the contribution of the non-linear term becomes comparable (in the sense of mean squares) with that of the linear term. The method has proved to be efficient for two simple bifurcation models (period doubling bifurcation and pitchfork bifurcation) and might be helpful in application to geophysics problems. The transition of a nonlinear system through the bifurcation point offers a new opportunity for estimating the internal noise using the magnitude of the noisedependent hysteretic loop, which occurs when the control parameter is changed in the forward and backward direction.

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“…The estimates presented above, are in good agreement with the results of numerical simulation, performed in (Kravtsov and Surovyatkina, 2003) and shown by a continuous line at Fig. 1.…”

Section: Prebifurcation Noise Amplification At the Threshold Of Periosupporting

confidence: 86%

“…This is true not only for period-doubling bifurcations (Kravtsov and Surovyatkina, 2003), but also for pitchfork bifurcations.…”

Section: On Weak Noise Measurements On Basis Of Nonlinear Saturation mentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems

Surovyatkina

2005

Nonlin. Processes Geophys.

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“…We illustrate, for the first time, the failure of the linear analysis through an order analysis, which reveals that the range of validity for the linear analysis is extremely limited and dramatically shrinks to zero as the bifurcation point is approached. We also explain the saturation of amplification previously observed in [13,14] using the developed scaling law.…”

Section: Introductionmentioning

confidence: 67%

“…Suppose that a fixed point of the map experiences a supercritical period-doubling bifurcation when the control parameter μ passes through a critical value μ bif . Near onset of the bifurcation, the system is sensitive to small alternating perturbations, applied to μ [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Under such alternating perturbations, the governing map becomes…”

Section: Introductionmentioning

confidence: 99%

Small-signal amplification of period-doubling bifurcations in smooth iterated maps

et al. 2006

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Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.

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