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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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Chaos and gauge field theory /Tamas S. Biró, Sergei Gaykovich Matinyan, Berndt Müller
Singapore : World Scientific, 1994
ix, 288 pages. : illustrations ; 23 cm
Ký hiệu phân loại (DDC): 003.8
An examination of current research into the dynamical properties of elementary fields. This book is divided into two parts: the first dealing with the "classical" discovery of chaos in gauge field theory and the second presenting methods and research achievements in recent years.
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Chaos in chemistry and biochemistry / [Edited by] Richard J Field; László Györgyi
Singapore ; River Edge, NJ : World Scientific, 1993
289 p. : illustrations ; 22 cm.
Ký hiệu phân loại (DDC): 541.394
True deterministic chaos is characterized by unpredictable, apparently random motion in a dynamical system completely described by a deterministic dynamic law, usually a nonlinear differential equation, with no stochastic component. The inability to predict future behavior of a chaotic system occurs because trajectories evolving from arbitrarily close initial conditions diverge. Chaos is universal as it may arise in any system governed by one of a class of quite common, suitable nonlinear dynamic laws. This book discusses both the experimental observation and theoretical interpretation of chaos in chemical and biochemical systems. Examples are drawn from the Belousov-Zhabotinsky reaction, surface reactions, electrochemical reactions, enzyme reactions, and periodically perturbed oscillating systems.
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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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