Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson.
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 sys...
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Superior document: | World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
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Year of Publication: | 2010 |
Language: | English |
Series: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
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Physical Description: | xv, 238 p. :; ill. (some col.). |
Notes: | Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. |
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Simpson, David John Warwick. Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson. New Jersey : World Scientific, 2010. xv, 238 p. : ill. (some col.). World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. Includes bibliographical references (p. 215-235) and index. 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. Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. Bifurcation theory. Differential equations. Saccharomyces cerevisiae. Electronic books. ProQuest (Firm) World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70. https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=731331 Click to View |
language |
English |
format |
Electronic eBook |
author |
Simpson, David John Warwick. |
spellingShingle |
Simpson, David John Warwick. Bifurcations in piecewise-smooth continuous systems World Scientific series on nonlinear science. Series A, Monographs and treatises ; |
author_facet |
Simpson, David John Warwick. ProQuest (Firm) ProQuest (Firm) |
author_variant |
d j w s djw djws |
author2 |
ProQuest (Firm) |
author2_role |
TeilnehmendeR |
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ProQuest (Firm) |
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Simpson, David John Warwick. |
title |
Bifurcations in piecewise-smooth continuous systems |
title_full |
Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson. |
title_fullStr |
Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson. |
title_full_unstemmed |
Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson. |
title_auth |
Bifurcations in piecewise-smooth continuous systems |
title_new |
Bifurcations in piecewise-smooth continuous systems |
title_sort |
bifurcations in piecewise-smooth continuous systems |
series |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; |
series2 |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; |
publisher |
World Scientific, |
publishDate |
2010 |
physical |
xv, 238 p. : ill. (some col.). |
isbn |
9789814293853 (electronic bk.) |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA380 |
callnumber-sort |
QA 3380 S56 42010 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=731331 |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.35 |
dewey-sort |
3515.35 |
dewey-raw |
515.35 |
dewey-search |
515.35 |
oclc_num |
670429733 |
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World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
hierarchy_sequence |
v. 70. |
is_hierarchy_title |
Bifurcations in piecewise-smooth continuous systems |
container_title |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
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