Bifurcations in piecewise-smooth continuous systems
By: David John Warwick Simpson
Series: World Scientific series on nonlinear science. Series A, Monographs and treatises -- v. 70; World Scientific series on nonlinear science -- v. 70.
Publisher: World Scientific
Published: 2010
Place of publication: New Jersey
Language: eng
Number of pages: 238
ISBN-13: 9789814293846
Subjects: Differential equations; Bifurcation theory; Saccharomyces cerevisiae
Description: 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.
Notes: Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.

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