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...

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Tác giả chính: Simpson, David John Warwick
Tác giả của công ty: ebrary, Inc
Định dạng: Điện tử eBook
Ngôn ngữ:Tiếng Anh
Được phát hành: New Jersey : World Scientific, 2010.
Loạt:World Scientific series on nonlinear science. Monographs and treatises ; v. 70.
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Truy cập trực tuyến:An electronic book accessible through the World Wide Web; click to view
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Tóm tắt: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.
Mô tả sách:Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
Mô tả vật lý:xv, 238 p. : ill. (some col.).
Thư mục:Includes bibliographical references (p. 215-235) and index.