Bifurcations in piecewise-smooth continuous systems
by Simpson, David John Warwick
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 mathemati…
Read More ↓Title Statements
- Full title :Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson
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
Read More ↓Edition Statements
- Publication Date:2010
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:New Jersey
- Language:eng
- Publication Date:2010
Notes
Originally presented as: Thesis (Ph. D.)--University of Colorado at Boulder, 2008
The Physical Object
- Description:1 online resource (xv, 238 p.) : illustrations (some color)
Edition Identifiers
- ISBN:9789814293846, 9814293849, 9789814293853, 9814293857
- oclc:ocn897038920
- LC Classification:QA380
- Dewey Decimal:515.35
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