Bifurcations in piecewise-smooth continuous systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
2010
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 70 |
| Schlagworte: | |
| Beschreibung: | Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008 Includes bibliographical references (p. 215-235) and index 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 |
| Beschreibung: | xv, 238 p. |
| ISBN: | 9789814293846 9814293849 9789814293853 |
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| 500 | |a Includes bibliographical references (p. 215-235) and index | ||
| 500 | |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 | ||
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Datensatz im Suchindex
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| id | DE-604.BV044156387 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:45:18Z |
| institution | BVB |
| isbn | 9789814293846 9814293849 9789814293853 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029563232 |
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| physical | xv, 238 p. |
| psigel | ZDB-30-PAD |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| series2 | World Scientific series on nonlinear science |
| spelling | Simpson, David John Warwick Verfasser aut Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson New Jersey World Scientific 2010 xv, 238 p. txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 70 Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008 Includes bibliographical references (p. 215-235) and index 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 Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simpson, David John Warwick Bifurcations in piecewise-smooth continuous systems Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Bifurcations in piecewise-smooth continuous systems |
| title_auth | Bifurcations in piecewise-smooth continuous systems |
| title_exact_search | Bifurcations in piecewise-smooth continuous systems |
| title_full | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_fullStr | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_full_unstemmed | Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson |
| title_short | Bifurcations in piecewise-smooth continuous systems |
| title_sort | bifurcations in piecewise smooth continuous systems |
| topic | Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik |
| work_keys_str_mv | AT simpsondavidjohnwarwick bifurcationsinpiecewisesmoothcontinuoussystems |