Reconstruction of complex dynamical systems affected by strong measurement noise.

This Letter reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured time series and proper data analysis. Finally, real world data sets are presented pointing out the relevance of the new approach.

[1]  Tom Kuusela,et al.  Stochastic heart-rate model can reveal pathologic cardiac dynamics. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  J. Peinke,et al.  Evidence of Markov properties of high frequency exchange rate data , 2001 .

[3]  Murat Tutkun,et al.  Markovian properties of passive scalar increments in grid-generated turbulence , 2004 .

[4]  P. Sura,et al.  A note on estimating drift and diffusion parameters from timeseries , 2002 .

[5]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[6]  J. Peinke,et al.  Stochastic analysis of different rough surfaces , 2004 .

[7]  J Peinke,et al.  Comment on "Indispensable finite time corrections for Fokker-Planck equations from time series data". , 2002, Physical review letters.

[8]  H. Risken.  Fokker-Planck Equation , 1984 .

[9]  R. Friedrich,et al.  On a quantitative method to analyze dynamical and measurement noise , 2003 .

[10]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[11]  Schreiber,et al.  Noise reduction in chaotic time-series data: A survey of common methods. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Joachim Peinke,et al.  Experimental indications for Markov properties of small-scale turbulence , 2001, Journal of Fluid Mechanics.

[13]  Jan Raethjen,et al.  Extracting model equations from experimental data , 2000 .

[14]  H Kantz,et al.  Indispensable finite time corrections for Fokker-Planck equations from time series data. , 2001, Physical review letters.

[15]  Stark,et al.  Estimation of noise levels for models of chaotic dynamical systems , 2000, Physical review letters.

[16]  Gradisek,et al.  Analysis of time series from stochastic processes , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  J. Peinke,et al.  Description of a Turbulent Cascade by a Fokker-Planck Equation , 1997 .

[18]  G. Ryskin,et al.  Simple procedure for correcting equations of evolution: Application to Markov processes , 1997 .

[19]  J. Peinke,et al.  Reconstruction of the Deterministic Dynamics of Stochastic Systems , 2004, Int. J. Bifurc. Chaos.

[20]  R. Friedrich,et al.  Reconstruction of dynamical equations for traffic flow , 2002 .