Bifurcations in piecewise-smooth continuous systems

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Tác giả: David John Warwick Simpson

Ngôn ngữ: eng

ISBN-13: 978-9814293846

ISBN-10: 9814293849

Ký hiệu phân loại: 515.35 Differential equations

Thông tin xuất bản: New Jersey : World Scientific, 2010.

Mô tả vật lý: xv, 238 p. : , ill. (some col.) ; , 24 cm.

Bộ sưu tập: Khoa học tự nhiên

ID: 350506

 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.
Includes bibliographical references (p. 215-235) and index.
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