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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| Autor Principal: | |
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| Formato: | Libro |
| Idioma: | English |
| Publicado: |
New Jersey :
World Scientific,
2010.
|
| Series: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 70. |
| Materias: | |
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| 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 xv, 238 p. : |b il. (algunas col.) ; |c 24 cm. | ||
| 490 | 1 | |a World Scientific series on nonlinear science. Series A, Monographs and treatises ; |v v. 70 | |
| 500 | |a Originally presented as: Thesis (Ph.D.)--University of Colorado at Boulder, 2008. | ||
| 504 | |a Incluye referencias bibliográficas (p. 215-235) e índice. | ||
| 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. | ||
| 020 | |a 9789814293846 | ||
| 020 | |a 9814293849 | ||
| 100 | 1 | |a Simpson, David John Warwick. | |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 70. | |
| 650 | 0 | |a Bifurcation theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Saccharomyces cerevisiae. | |
| 084 | |a 37Gxx (92C99) |2 msc2000 | ||
| 010 | |a 2010484011 | ||
| 040 | |a BTCTA |b eng |c BTCTA |d YDXCP |d FQG |d BWX |d TXA |d SINLB |d DLC | ||
| 859 | |h 37 |i Si613 |p A-8667 |b BIB. MATEMATICA | ||