Currie, Anthony (1987) Chaotic dynamics in flows and discrete maps. PhD thesis, University of Warwick.

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Abstract

This work attempts to utilise perturbation theory to derive discrete mappings which describe the dynamical behaviour of a continuous, and a discrete, chaotic system.

The first three chapters introduce some background to the theory of chaotic behaviour In discrete and continuous systems. Chapter 4 considers the dynamical behaviour of Duffings equation. Perturbation theory is applied to Hamiltonian solutions of the system, and a 1-D mapping is derived which models the bifurcation of the system to chaos. Chapter 5 introduces a 2-D chaotic difference map. The qualitative dynamics of the system are investigated and a form of perturbation theory is applied to a parameterised version of the map. The perturbative solutions are shown to exhibit dynamical behaviour very like the original system.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Perturbation (Mathematics), Chaotic behavior in systems, Duffing equations
Official Date:	January 1987
Dates:	Date Event January 1987 Submitted
Institution:	University of Warwick
Theses Department:	Department of Physics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Rowlands, G. (George)
Sponsors:	Science and Engineering Research Council (Great Britain)
Format of File:	pdf
Extent:	vii, 127 leaves : illustrations
Language:	eng

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