Bifurcations and chaos in piecewise-smooth dynamical systems /
Saved in:
| Author / Creator: | Zhusubaliyev, Zhanybai T. |
|---|---|
| Imprint: | River Edge, New Jersey : World Scientific, c2003. |
| Description: | 363 p. : ill. ; 27 cm. |
| Language: | English |
| Series: | World Scientific series on Nonlinear science. Series A ; v.44 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v.44. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4956375 |
| Summary: | 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. |
|---|---|
| Physical Description: | 363 p. : ill. ; 27 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9812384200 |
