World Scientific Series On Nonlinear Science Series A: Bifurcations In Piecewise-smooth Continuous Systems (PDF)
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autor: David John Warwick Simpson
- 2010, 256 Seiten, Englisch
- Verlag: World Scientific Publishing Company
- ISBN-10: 9814293857
- ISBN-13: 9789814293853
- Erscheinungsdatum: 13.01.2010
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- Größe: 11 MB
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Englisch
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