Hidden Bibliographic Details
| ISBN: | 9789814293853
9814293857
9789814293846
9814293849
1282763423
9781282763425
9786612763427
6612763426
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| Digital file characteristics: | data file
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| Notes: | Includes bibliographical references and index.
English.
Print version record.
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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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| Other form: | Print version: Simpson, David John Warwick. Bifurcations in piecewise-smooth continuous systems. Singapore ; Hackensack, NJ : World Scientific, 2010 9814293849
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