Bifurcations in piecewise-smooth continuous systems
Title:
Bifurcations in piecewise-smooth continuous systems
Author:
Simpson, David John Warwick
ISBN:
9789814293846
Publication Information:
Singapore : World Scientific, 2010
Physical Description:
xv, 238 p. : ill. (some col.) ; 24 cm.
Series:
World Scientific series on nonlinear science. Series A, Monographs and treatises ; 70
World Scientific series on nonlinear science
Series Title:
World Scientific series on nonlinear science. Series A, Monographs and treatises ;
World Scientific series on nonlinear science
General Note:
Includes bibliographical references (p. 215-235) and index
Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008
Abstract:
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.
Subject:
| Bifurcation theory |
| Differential equations |
| Saccharomyces cerevisiae |
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.