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.
NeimarkSacker-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.
| Autorius: | David John Warwick Simpson |
| Leidėjas: | World Scientific |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 256 |
| ISBN-10: | 9814293849 |
| ISBN-13: | 9789814293846 |
| Formatas: | 235 x 157 x 18 mm. Knyga kietu viršeliu |
| Kalba: | Anglų |
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