Bifurcations in piecewise-smooth continuous systems
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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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey :
World Scientific,
2010.
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| Series: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
| Subjects: | |
| Online Access: | An electronic book accessible through the World Wide Web; click to view |
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| 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.). |
| Bibliography: | Includes bibliographical references (p. 215-235) and index. |