| Description |
1 online resource (xv, 238 pages) : illustrations (some color). |
| Physical Medium |
polychrome |
| Description |
text file |
| 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. |
| 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. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Bifurcation theory.
|
|
Bifurcation theory. |
|
Differential equations.
|
|
Differential equations. |
|
Saccharomyces cerevisiae.
|
|
Saccharomyces cerevisiae. |
| Genre/Form |
Electronic books.
|
|
Electronic books.
|
| Other Form: |
Print version: Simpson, David John Warwick. Bifurcations in piecewise-smooth continuous systems. Singapore ; Hackensack, NJ : World Scientific, 2010 9814293849 (OCoLC)496957923 |
| ISBN |
9789814293853 (electronic book) |
|
9814293857 (electronic book) |
|
9789814293846 |
|
9814293849 |
|
