Bifurcations and chaos in piecewise-smooth dynamical systems:
Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large va...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2003
|
| Schriftenreihe: | World Scientific series on nonlinear science. Series A
v. 44 |
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| Zusammenfassung: | Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory. The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general |
| Beschreibung: | xii, 363 p. ill |
| ISBN: | 9789812564436 |
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| 520 | |a Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory. The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general | ||
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Datensatz im Suchindex
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| id | DE-604.BV044633994 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:43Z |
| institution | BVB |
| isbn | 9789812564436 |
| language | English |
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| physical | xii, 363 p. ill |
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| series2 | World Scientific series on nonlinear science. Series A |
| spelling | Zhusubaliyev, Zhanybai T. Verfasser aut Bifurcations and chaos in piecewise-smooth dynamical systems Zhanybai T. Zhusubaliyev, Erik Mosekilde Singapore World Scientific Pub. Co. c2003 xii, 363 p. ill txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science. Series A v. 44 Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory. The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems Mosekilde, Erik Sonstige oth Erscheint auch als Druck-Ausgabe 9789812384201 Erscheint auch als Druck-Ausgabe 9812384200 http://www.worldscientific.com/worldscibooks/10.1142/5313#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Zhusubaliyev, Zhanybai T. Bifurcations and chaos in piecewise-smooth dynamical systems Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems |
| title | Bifurcations and chaos in piecewise-smooth dynamical systems |
| title_auth | Bifurcations and chaos in piecewise-smooth dynamical systems |
| title_exact_search | Bifurcations and chaos in piecewise-smooth dynamical systems |
| title_full | Bifurcations and chaos in piecewise-smooth dynamical systems Zhanybai T. Zhusubaliyev, Erik Mosekilde |
| title_fullStr | Bifurcations and chaos in piecewise-smooth dynamical systems Zhanybai T. Zhusubaliyev, Erik Mosekilde |
| title_full_unstemmed | Bifurcations and chaos in piecewise-smooth dynamical systems Zhanybai T. Zhusubaliyev, Erik Mosekilde |
| title_short | Bifurcations and chaos in piecewise-smooth dynamical systems |
| title_sort | bifurcations and chaos in piecewise smooth dynamical systems |
| topic | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems |
| topic_facet | Bifurcation theory Chaotic behavior in systems Differentiable dynamical systems |
| url | http://www.worldscientific.com/worldscibooks/10.1142/5313#t=toc |
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