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Computing Global Decompositions of Dynamical Systems

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Date Issued:
2006
Summary:
In this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's Lyapunov function. We used the C++ language to code the algorithm.
Title: Computing Global Decompositions of Dynamical Systems.
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Name(s): Ban, Hyunju, author
Kalies, William D., Thesis advisor
Florida Atlantic University, Degree grantor
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2006
Date Issued: 2006
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 173 p.
Language(s): English
Summary: In this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting approximations of attractor-repeller pairs, invariant sets, and Conley's Lyapunov function. We used the C++ language to code the algorithm.
Identifier: FA00000848 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2006.
Subject(s): Lyapunov functions
Control theory
Mathematical optimization
Differentiable dynamical systems
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00000848
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.