Bifurcations in piecewise-smooth continuous systems /

Bifurcations in piecewise-smooth continuous systems /

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Bibliographic Details
Author / Creator:	Simpson, David John Warwick.
Imprint:	Singapore ; Hackensack, NJ : World Scientific, 2010.
Description:	xv, 238 p. : ill. (some col.) ; 24 cm.
Language:	English
Series:	World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70.
Subject:	Bifurcation theory. Differential equations. Saccharomyces cerevisiae. Bifurcation theory. Differential equations. Saccharomyces cerevisiae.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8056368

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ISBN:	9814293849 9789814293846
Notes:	Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. Includes bibliographical references and index.
Summary:	Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

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Call Number:	QA380 .S55 2010
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