TY  - BOOK
AU  - Simpson,David John Warwick
ED  - ebrary, Inc.
TI  - Bifurcations in piecewise-smooth continuous systems
T2  - World Scientific series on nonlinear science. Series A, Monographs and treatises
AV  - QA380 .S56 2010eb
U1  - 515.35 22
PY  - 2010///
CY  - New Jersey
PB  - World Scientific
KW  - Bifurcation theory
KW  - Differential equations
KW  - Saccharomyces cerevisiae
KW  - Electronic books
KW  - local
N1  - Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008; Includes bibliographical references (p. 215-235) and index; Electronic reproduction; Palo Alto, Calif.; ebrary; 2013; Available via World Wide Web; Access may be limited to ebrary affiliated libraries
N2  - 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
UR  - http://site.ebrary.com/lib/daystar/Doc?id=10422400
ER  -