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By James B. Kadtke, Yurii A. Kravtsov (auth.), Professor Dr. Yurii A. Kravtsov, Dr. James B. Kadtke (eds.)

ISBN-10: 3642802540

ISBN-13: 9783642802546

ISBN-10: 3642802567

ISBN-13: 9783642802560

This is a publication booklet for researchers and practitioners attracted to modeling, prediction and forecasting of normal platforms in response to nonlinear dynamics. it's a useful advisor to info research and to the improvement of algorithms, particularly for complicated structures. issues akin to the characterization of nonlinear correlations in information as dynamical structures, reconstruction of dynamical versions from information, nonlinear noise aid and the boundaries of predicatability are mentioned. The chapters are written by means of best specialists and view useful difficulties reminiscent of sign and time sequence research, biomedical information research, monetary research, stochastic modeling, human evolution, and political modeling. The publication contains new tools for nonlinear filtering of advanced indications, new algorithms for sign class, and the idea that of the "Global Brain".

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Extra info for Predictability of Complex Dynamical Systems

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In the problem of distinguishing between these two distinct cases, it is therefore useful, possibly even necessary, to perform chaotic noise reduction. It seems prudent to add the following caveat. As is well-known, some deterministic systems may be high dimensional, and appear pretty noisy. If they have too many degrees of freedom, it may be necessary or even best to regard them as effectively random for all practical purposes. Indeed the effort to use the data analysis methods developed for nonlinear dynamics only makes sense when the system is low dimensional.

1993): Chaos 2, 127. , and Pignataro, T. (1982): Phys. Rev. A 25, 3453. V. (1985): J. Opt. Soc. America, B2,552. , and Tang, D. (1993): in Time Series Prediction: Forecasting the Future and Understanding the Past (ed. S. A. Gershenfeld). Addison-Wesley, Reading, Mass. 73. , and Glass, L. (1992): Phys. Rev. Lett. 68,427); and Physica D 64, 43l. I. (1992): Phys. Rev. A 45, 3403. Kostelich, E. A. (1988): Phys. Rev. A 38, 1649. J. and Schreiber, T. (1993): Phys. Rev. E 48,1752. B. H. Freeman. , and Provenzale, A.

This is as we would like to have it in an unforgiving test. But, paradoxically, by admitting noise-reduced versions of a data set for analysis, we actually can tighten those tolerances. Summarizing, by examining noise-reduced versions of a time series, we can enlarge the effective class of datasets eligible for a determinism call; and we are able also to set more exacting and unforgiving tolerances on our criteria for phase portrait smoothness. In other words, integration of the use of chaotic noise reduction into our approach provides a way for us to rule more strictly against Ko (fewer false alarms) and, at the same time, give the matter our best shot (more detections)!

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Predictability of Complex Dynamical Systems by James B. Kadtke, Yurii A. Kravtsov (auth.), Professor Dr. Yurii A. Kravtsov, Dr. James B. Kadtke (eds.)


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