Bifurcations in piecewise-smooth continuous systems [electronic resource] / David John Warwick Simpson.
By: Simpson, David John Warwick.
Contributor(s): ebrary, Inc.
Material type:
BookSeries: World Scientific series on nonlinear scienceSeries AMonographs and treatises: v. 70.Publisher: New Jersey : World Scientific, 2010Description: xv, 238 p. : ill. (some col.) ; 24 cm.Subject(s): Bifurcation theory | Differential equations | Saccharomyces cerevisiaeGenre/Form: Electronic books.DDC classification: 515.35 Online resources: An electronic book accessible through the World Wide Web; click to view 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.
Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
Includes bibliographical references (p. 215-235) and index.
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.
Electronic reproduction. Palo Alto, Calif. : ebrary, 2011. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.
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