Current Search: Ban, Hyunju (x)
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Title
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Computing Global Decompositions of Dynamical Systems.
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Creator
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Ban, Hyunju, Kalies, William D., Florida Atlantic University
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Abstract/Description
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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...
Show moreIn 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.
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Date Issued
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2006
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PURL
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http://purl.flvc.org/fau/fd/FA00000848
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Subject Headings
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Lyapunov functions, Control theory, Mathematical optimization, Differentiable dynamical systems
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Format
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Document (PDF)
