Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson.
2010
QA380 .S56 2010eb
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Title
Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson.
Author
Simpson, David John Warwick.
ISBN
9789814293846
9814293849
9789814293853 (e-book)
9814293849
9789814293853 (e-book)
Publication Details
New Jersey : World Scientific, 2010.
Language
English
Description
xv, 238 p. : ill. (some col.) ; 24 cm.
Call Number
QA380 .S56 2010eb
Dewey Decimal Classification
515.35
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.
Note
Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
Bibliography, etc. Note
Includes bibliographical references (p. 215-235) and index.
Access Note
Access limited to authorized users.
Series
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70.
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