TY  - GEN
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.
AB  - 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.
T1  - Bifurcations in piecewise-smooth continuous systems
DA  - 2010.
CY  - New Jersey :
AU  - Simpson, David John Warwick.
VL  - v. 70
CN  - QA380
PB  - World Scientific,
PP  - New Jersey :
PY  - 2010.
N1  - Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
ID  - 418205
KW  - Bifurcation theory.
KW  - Differential equations.
KW  - Saccharomyces cerevisiae.
TI  - Bifurcations in piecewise-smooth continuous systems
LK  - https://univsouthin.idm.oclc.org/login?url=http://site.ebrary.com/lib/usiricelib/Doc?id=10422400
UR  - https://univsouthin.idm.oclc.org/login?url=http://site.ebrary.com/lib/usiricelib/Doc?id=10422400
ER  -