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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2010.
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| Colección: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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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| Descripción Física: | 1 online resource (xv, 238 pages) : illustrations (some color) |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9789814293853 9814293857 1282763423 9781282763425 9786612763427 6612763426 |