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Bifurcations in piecewise-smooth continuous systems /
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 sys...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2010.
|
| Colección: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Simpson, David John Warwick. | |
| 245 | 1 | 0 | |a Bifurcations in piecewise-smooth continuous systems / |c David John Warwick Simpson. |
| 260 | |a New Jersey : |b World Scientific, |c ©2010. | ||
| 300 | |a 1 online resource (xv, 238 pages) : |b illustrations (some color) | ||
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| 490 | 1 | |a World Scientific series on nonlinear science. Series A, Monographs and treatises ; |v v. 70 | |
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Bifurcation theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Saccharomyces cerevisiae. | |
| 650 | 2 | |a Saccharomyces cerevisiae | |
| 650 | 6 | |a Théorie de la bifurcation. | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Saccharomyces cerevisiæ. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Bifurcation theory |2 fast | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Saccharomyces cerevisiae |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Simpson, David John Warwick. |t Bifurcations in piecewise-smooth continuous systems. |d Singapore ; Hackensack, NJ : World Scientific, 2010 |z 9814293849 |w (OCoLC)496957923 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 70. | |
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