Bifurcations in piecewise-smooth continuous systems:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey
World Scientific
©2010
|
| Series: | World Scientific series on nonlinear science
v. 70 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Originally presented as: Thesis (Ph. D.)--University of Colorado at Boulder, 2008 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 Includes bibliographical references and index |
| Physical Description: | 1 Online-Ressource (xv, 238 pages) |
| ISBN: | 9789814293846 9789814293853 9814293849 9814293857 |
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| 490 | 0 | |a World Scientific series on nonlinear science |v v. 70 | |
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| 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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| indexdate | 2024-07-10T07:18:35Z |
| institution | BVB |
| isbn | 9789814293846 9789814293853 9814293849 9814293857 |
| language | English |
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| spelling | Simpson, David John Warwick Verfasser aut Bifurcations in piecewise-smooth continuous systems David John Warwick Simpson New Jersey World Scientific ©2010 1 Online-Ressource (xv, 238 pages) 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 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 Includes bibliographical references and index Mathematics MATHEMATICS / Differential Equations / General bisacsh Mathematik 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 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340685 Aggregator 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 Mathematics MATHEMATICS / Differential Equations / General bisacsh Mathematik 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 | Mathematics MATHEMATICS / Differential Equations / General bisacsh Mathematik Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Mathematics MATHEMATICS / Differential Equations / General Mathematik Bifurcation theory Differential equations Saccharomyces cerevisiae Verzweigung Mathematik |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340685 |
| work_keys_str_mv | AT simpsondavidjohnwarwick bifurcationsinpiecewisesmoothcontinuoussystems |