Bifurcations in piecewise-smooth continuous systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey
World Scientific
2010
|
| Series: | World Scientific series on nonlinear science
v. 70 |
| Subjects: | |
| Item Description: | 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 |
| Physical Description: | xv, 238 p. |
| ISBN: | 9789814293846 9814293849 9789814293853 |
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| id | DE-604.BV044156387 |
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| indexdate | 2024-07-10T07:45:18Z |
| institution | BVB |
| isbn | 9789814293846 9814293849 9789814293853 |
| language | English |
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| physical | xv, 238 p. |
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| publishDateSearch | 2010 |
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| publisher | World Scientific |
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| 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 |