PMID: 22587170May 17, 2012Paper

Random dynamical models from time series

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Y I MolkovA M Feigin

Abstract

In this work we formulate a consistent Bayesian approach to modeling stochastic (random) dynamical systems by time series and implement it by means of artificial neural networks. The feasibility of this approach for both creating models adequately reproducing the observed stationary regime of system evolution, and predicting changes in qualitative behavior of a weakly nonautonomous stochastic system, is demonstrated on model examples. In particular, a successful prognosis of stochastic system behavior as compared to the observed one is illustrated on model examples, including discrete maps disturbed by non-Gaussian and nonuniform noise and a flow system with Langevin force.

References

Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R Meyer, N Christensen
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B P Bezruchko, D A Smirnov
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S GüttlerE Olbrich
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dmitry A SmirnovYevgeny P Seleznev
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E BagarinaoS Sato
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Apr 20, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V F Pisarenko, D Sornette
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D N MukhinYa I Molkov
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E M LoskutovA M Feigin
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Y I MolkovA M Feigin

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Citations

Sep 9, 2016·Physiological Reports·Ekaterina MorozovaYaroslav Molkov
Oct 23, 2015·Scientific Reports·Dmitry MukhinJuergen Kurths
Sep 8, 2017·American Journal of Physiology. Regulatory, Integrative and Comparative Physiology·Abolhassan BehrouzvaziriYaroslav I Molkov
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dmitry A Smirnov, Igor I Mokhov
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dmitry A Smirnov
May 16, 2019·Scientific Reports·Dmitry MukhinAlexander Feigin

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