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 |
|---|---|
| : | |
| TeilnehmendeR: | |
| Year of Publication: | 2010 |
| Language: | English |
| Series: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
| Online Access: | |
| 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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| 100 | 1 | |a Simpson, David John Warwick. | |
| 245 | 1 | 0 | |a Bifurcations in piecewise-smooth continuous systems |h [electronic resource] / |c David John Warwick Simpson. |
| 260 | |a New Jersey : |b World Scientific, |c 2010. | ||
| 300 | |a xv, 238 p. : |b ill. (some col.). | ||
| 490 | 1 | |a World Scientific series on nonlinear science. Series A, Monographs and treatises ; |v v. 70 | |
| 500 | |a Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. | ||
| 504 | |a Includes bibliographical references (p. 215-235) and index. | ||
| 520 | |a 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. | ||
| 533 | |a Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. | ||
| 650 | 0 | |a Bifurcation theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Saccharomyces cerevisiae. | |
| 655 | 4 | |a Electronic books. | |
| 710 | 2 | |a ProQuest (Firm) | |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 70. | |
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=731331 |z Click to View |