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...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2010
|
| Schriftenreihe: | World Scientific series on nonlinear science. Series A, Monographs and treatises
v. 70 |
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | 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. ill. (some col.) |
| ISBN: | 9789814293853 |
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| 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 | ||
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Datensatz im Suchindex
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| author | Simpson, David John Warwick |
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| author_sort | Simpson, David John Warwick |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044637980 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:57:52Z |
| institution | BVB |
| isbn | 9789814293853 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030035952 |
| oclc_num | 1012628468 |
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| physical | xv, 238 p. ill. (some col.) |
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| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | World Scientific Pub. Co. |
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| series2 | World Scientific series on nonlinear science. Series A, Monographs and treatises |
| spelling | Simpson, David John Warwick Verfasser aut Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson Singapore World Scientific Pub. Co. c2010 xv, 238 p. ill. (some col.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science. Series A, Monographs and treatises v. 70 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 Differential equations Bifurcation theory Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789814293846 Erscheint auch als Druck-Ausgabe 9814293849 http://www.worldscientific.com/worldscibooks/10.1142/7612#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simpson, David John Warwick Bifurcations in piecewise-smooth continuous systems Differential equations Bifurcation theory 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 | Differential equations Bifurcation theory Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Differential equations Bifurcation theory Saccharomyces cerevisiae Verzweigung Mathematik |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7612#t=toc |
| work_keys_str_mv | AT simpsondavidjohnwarwick bifurcationsinpiecewisesmoothcontinuoussystems |