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…
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- 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.
The Physical Object
- Description:1 online resource (xv, 238 pages) : : illustrations (some color)
Edition Identifiers
- ISBN:9789814293853, 9814293857, 1282763423, 9781282763425, 9786612763427, 6612763426
- oclc:ocn670429733
- LC Classification:QA380
- Dewey Decimal:515.35
Table of Contents
Preface; Acknowledgments; Contents; 1. Fundamentals of Piecewise-Smooth, Continuous Systems; 2. Discontinuous Bifurcations in Planar Systems; 3. Codimension-Two, Discontinuous Bifurcations; 4. The Growth of Saccharomyces cerevisiae; 5. Codimension-Two, Border-Collision Bifurcations; 6. Periodic Solutions and Resonance Tongues; 7. Neimark-Sacker-Like Bifurcations; Appendix A Selected Proofs; Appendix B Additional Figures; Appendix C Adjugate Matrices; Appendix D Parameter Values for S. cerevisiae; Bibliography; Index
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