Possibility of measuring weak noise in nonlinear systems

Elena D. Surovyatkina

doi:10.1117/12.546909

25 May 2004 Possibility of measuring weak noise in nonlinear systems

Elena D. Surovyatkina

Proceedings Volume 5471, Noise in Complex Systems and Stochastic Dynamics II; (2004) https://doi.org/10.1117/12.546909
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain

Abstract

The possibility of measuring weak noise in nonlinear systems on the basis of the phenomenon of prebifurcation noise amplification is proposed. This phenomenon is shortly outlined with special emphasis on the transition from linear regime to the regime of nonlinear saturation of fluctuation amplification. Estimates of the fluctuation variance are obtained both for the linear (away from the bifurcation threshold) and for the nonlinear regime (in the vicinity of the bifurcation threshold). These estimates have proved to be efficient for two simple bifurcation models: period doubling bifurcation and bifurcation of spontaneous symmetry breaking. Theoretical estimates have proved to be in good agreement with the results of numerical simulation. It is shown, that in the saturation regime, fluctuation variance is proportional to the square root of external noise variance, whereas in linear regime, fluctuation variance is proportional to noise variance. The approach to weak noise measuring is based on comparison of maximal fluctuation variance at the bifurcation threshold with variance away from that threshold. The applicability of this approach is limited by the necessity to perform rather long-term observations.

Citation Download Citation

Elena D. Surovyatkina "Possibility of measuring weak noise in nonlinear systems", Proc. SPIE 5471, Noise in Complex Systems and Stochastic Dynamics II, (25 May 2004); https://doi.org/10.1117/12.546909

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