"Nonlinear dynamics has become an important tool in the analysis and modeling of biological systems. The tendency for biological systems to be both very noisy and non- stationary has severely limited the application of traditional nonlinear techniques to these systems. New analysis methods based on topologically invariant properties of nonlinear dynamical systems have been successful in overcoming some of the difficulties presented by both noise and non-stationarity.
Two such methods, the unstable periodic orbit (UPO) detection algorithm and the noisy precursor detection algorithm, are presented here. The UPO detection algorithm provides a method both for detecting low-dimensional dynamics in noisy data and for extracting dynamical information from such a system. The noisy precursor detection algorithm provides a new method for detecting precursors to instabilities in stable, but non-stationary, noisy systems. Both of these algorithms are demonstrated to be very robust to the presence of dynamical noise and are also capable of operating on extremely short data files.
This work also addresses many of the confusing issues that arise when using surrogate data to perform statistical hypothesis testing with these algorithms. The UPO detection algorithm in particular is shown to be insensitive to linear correlations in data. A new surrogate algorithm which avoids many of the difficulties associated with the surrogate algorithms currently used in nonlinear analysis is also presented"--Abstract, page iii.
Moss, Frank, 1934-
Parris, Paul Ernest, 1954-
Roe, Robert Paul
Ph. D. in Physics
University of Missouri--Rolla
viii, 63 pages
© 2000 Kevin Thomas Dolan, All rights reserved.
Dissertation - Restricted Access
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Electronic access to the full-text of this document is restricted to Missouri S&T users. Otherwise, request this publication directly from Missouri S&T Library or contact your local library.http://merlin.lib.umsystem.edu/record=b4514963~S5
Dolan, Kevin Thomas, "Analysis of biological and physical systems using nonlinear topological methods" (2000). Doctoral Dissertations. 1363.
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