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Bifurcations and chaos in piecewise-smooth dynamical systems /Zhanybai T. Zhusubaliyev, Erik Mosekilde
Singapore : World Scientific, 2003
xii, 363 pages. : illustrations ; 27 cm.
Ký hiệu phân loại (DDC): 515.3
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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Control of homoclinic chaos by weak periodic perturbations /Ricardo Chacón.
New Jersey ; London : World Scientific, 2005.
xiii, 223 pages. : ill. ; 24 cm.
Ký hiệu phân loại (DDC): 515.39
This monograph presents the theory of a chaos control method: suppression-enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The applications of the theory presented include control of chaotic solitons in Frenkel-Kontorova chains
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Modeling and computations in dynamical systems :in commemoration of the 100th anniversary of the birth of John von Neumann /Eusebius J. Doedel, Gábor Domokos, Ioannis G. Kevrekidis (editor)
Singapore ; London : World Scientific, 2006.
vi, 349 pages. : ill. (some col.) ; 29 cm.
Ký hiệu phân loại (DDC): 515.39
The Hungarian born mathematical genius, John von Neumann, was undoubtedly one of the greatest and most influential scientific minds of the 20th century. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J E Marsden, P J Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this book offers a unique combination of theoretical and appl
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Probability theory :a comprehensive course /Achim Klenke.
New York : Springer, 2013
633 pages. : illustrations
Ký hiệu phân loại (DDC): 519.2
Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms." "This text is a comprehensive course in modern probability theory and its
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