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Bifurcations in piecewise-smooth continuous systems / David John Warwick Simpson.
- Format:
- Book
- Author/Creator:
- Simpson, David John Warwick.
- Series:
- World Scientific series on nonlinear science. Monographs and treatises ; Series A, v. 70.
- World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70
- Language:
- English
- Subjects (All):
- Bifurcation theory.
- Differential equations.
- Saccharomyces cerevisiae.
- Physical Description:
- 1 online resource (256 p.)
- Edition:
- 1st ed.
- Place of Publication:
- New Jersey : World Scientific, 2010.
- Language Note:
- English
- 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.
- 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
- Notes:
- Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008.
- Includes bibliographical references (p. 215-235) and index.
- ISBN:
- 9786612763427
- 9781282763425
- 1282763423
- 9789814293853
- 9814293857
- OCLC:
- 670429733
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