Doctoral Dissertations

Abstract

"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.

Advisor(s)

Moss, Frank, 1934-

Committee Member(s)

Parris, Paul Ernest, 1954-
Fraundorf, Phillip
Wilemski, Gerald
Roe, Robert Paul

Department(s)

Physics

Degree Name

Ph. D. in Physics

Comments

Dissertation completed as part of a cooperative degree program with the University of Missouri--Rolla and the University of Missouri--St. Louis.

This work was supported by the U.S. Office of Naval Research, Physical Science Division.

Publisher

University of Missouri--Rolla

Publication Date

Summer 2000

Pagination

viii, 63 pages

Note about bibliography

Includes bibliographical references (pages 58-62).

Rights

© 2000 Kevin Thomas Dolan, All rights reserved.

Document Type

Dissertation - Restricted Access

File Type

text

Language

English

Subject Headings

AlgorithmsBiological systems

Thesis Number

T 7781

Print OCLC #

45965184

Electronic OCLC #

1107990923

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