Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson.
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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Superior document: | World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
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Anno di pubblicazione: | 2010 |
Lingua: | English |
Serie: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
Accesso online: | |
Descrizione fisica: | xv, 238 p. :; ill. (some col.). |
Note: | Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. |
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Riassunto: | 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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Bibliografia: | Includes bibliographical references (p. 215-235) and index. |
ISBN: | 9789814293846 9814293849 9789814293853 (electronic bk.) |
Hierarchical level: | Monograph |
Statement of Responsibility: | David John Warwick Simpson. |