Screen LibraryBifurcations in piecewise-smooth continuous systems
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| Main Authors: | |
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| Published: |
World Scientific,
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| Publisher Address: | Singapore Hackensack, NJ |
| Publication Dates: | 2010. |
| Literature type: | Book |
| Language: | English |
| Series: |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
| Subjects: | |
| Carrier Form: | xv, 238 p.: ill. (some col.) ; 24 cm. |
| ISBN: |
9814293849 9789814293846 |
| Index Number: | O177 |
| CLC: | O177.91 |
| Call Number: | O177.91/S613 |
| Contents: |
Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. Includes bibliographical references 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. |