| Description |
xv, 238 p. : ill. (some col.). |
| 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.
|
| Note |
Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. |
| Bibliography |
Includes bibliographical references (p. 215-235) 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. |
| Reproduction |
Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. |
| Subject |
Bifurcation theory.
|
|
Differential equations.
|
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Saccharomyces cerevisiae.
|
| Genre/Form |
Electronic books.
|
| Added Author |
ProQuest (Firm)
|
| ISBN |
9789814293846 |
|
9814293849 |
|
9789814293853 (electronic bk.) |
|
