Bifurcations in piecewise-smooth continuous systems /
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| Author / Creator: | Simpson, David John Warwick. |
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| 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: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8056368 |
| 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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| Item Description: | Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. |
| Physical Description: | xv, 238 p. : ill. (some col.) ; 24 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9814293849 9789814293846 |
