Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson.

• Superior document: World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70
• Author: ProQuest (Firm); Simpson, David John Warwick.
• TeilnehmendeR: ProQuest (Firm)
• Year of Publication: 2010
• Language: English
• Series: World Scientific series on nonlinear science. Monographs and treatises ; v. 70.
• Physical Description: xv, 238 p. :; ill. (some col.).
• Notes: Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
• Bibliography: Includes bibliographical references (p. 215-235) and index.
• ISBN: 9789814293846; 9814293849; 9789814293853 (electronic bk.)
• Hierarchical level: Monograph
• Statement of Responsibility: 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 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.