Practical Numerical Algorithms For Chaotic Systems
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Practical Numerical Algorithms For Chaotic Systems
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Author : Thomas S. Parker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Practical Numerical Algorithms For Chaotic Systems written by Thomas S. Parker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.
Practical Numerical Algorithms For Chaotic Systems
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Author : Thomas S Parker
language : en
Publisher:
Release Date : 1989-08-01
Practical Numerical Algorithms For Chaotic Systems written by Thomas S Parker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-01 with categories.
Chaos And Complexity In Nonlinear Electronic Circuits
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Author : Maciej J. Ogorza?ek
language : en
Publisher: World Scientific
Release Date : 1997
Chaos And Complexity In Nonlinear Electronic Circuits written by Maciej J. Ogorza?ek and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Science categories.
The basic procedures for designing and analysing electronic systems are based largely on the assumptions of linear behavior of the system. Nonlinearities inherent in all real applications very often cause unexpected and even strange behavior. This book presents an electronic engineer's perspective on chaos and complex behavior. It starts from basic mathematical notions which enable understanding of the observed phenomena, and guides the reader through the methodology and tools used in the laboratory and numerical experiments to interpretation and explanation of basic mechanisms. On typical circuit examples, it shows how the theoretical and empirical developments can be used in practice. Attention is drawn to applications of chaotic circuits as noise generators and the possible use of synchronized chaotic systems in information transmission and encryption. Chaos control is considered as a new, emerging area where electronic equipment and chaos theory could turn vital in biomedical and engineering issues.
Dynamical Chaos Models And Experiments Appearance Routes And Stru Of Chaos In Simple Dyna Systems
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Author : Vadim S Anishchenko
language : en
Publisher: World Scientific
Release Date : 1995-09-19
Dynamical Chaos Models And Experiments Appearance Routes And Stru Of Chaos In Simple Dyna Systems written by Vadim S Anishchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-19 with Science categories.
In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
Attractors Bifurcations Chaos
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Author : Tönu Puu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Attractors Bifurcations Chaos written by Tönu Puu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Mathematics categories.
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics chapters -on partial differential equations, and on bifurcations and catastrophe theory -thus making the mathematical background material fairly complete. The author is happy that this new book did rather well, but he preferred to rewrite it, rather than having just a new print run. Material, stemming from the first versions, was more than ten years old, while nonlinear dynamics has been a fast developing field, so some analyses looked rather old-fashioned and pedestrian. The necessary revision turned out to be rather substantial.
Engineering Applications Of Dynamics Of Chaos
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Author : W. Szemplinska-Stupnicka
language : en
Publisher: Springer
Release Date : 2014-05-04
Engineering Applications Of Dynamics Of Chaos written by W. Szemplinska-Stupnicka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
The treatment of chaotic dynamics in mathematics and physics during last two decades has led to a number of new concepts for the investigation of complex behavior in nonlinear dynamical processes. The aim the CISM course Engineering Applications of Dynamics of Chaos of which this is the proceedings volume was to make these concepts available to engineers and applied scientists possessing only such modest knowledges in mathematics which are usual for engineers, for example graduating from a Technical University. The contents of the articles contributed by leading experts in this field cover not only theoretical foundations and algorithmic and computational aspects but also applications to engineering problems. In the first article an introduction into the basic concepts for the investigation of chaotic behavior of dynamical systems is given which is followed in the second article by an extensive treatment of approximative analytical methods to determine the critical parameter values describing the onset of chaos. The important relation between chaotic dynamics and the phenomenon of turbulence is treated in the third article by studying instabilities various fluid flows. In this contribution also an introduction into interesting phenomenon of pattern formation is given. The fourth and fifth articles present various applications to nonlinear oscillations including roll motions of ships, rattling oscillations in gear boxes, tumbling oscillations of satellites, flutter motions of fluid carrying pipes and vibrations of robot arms. In the final article a short treatment of hyperchaos is given.
Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann
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Author : Eusebius Doedel
language : en
Publisher: World Scientific
Release Date : 2006-03-10
Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann written by Eusebius Doedel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-10 with Science categories.
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 applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics.The contents of this book was also published as a special issue of the International Journal of Bifurcation and Chaos — March 2005.
Essentials Of Nonlinear Circuit Dynamics With Matlab And Laboratory Experiments
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Author : Arturo Buscarino
language : en
Publisher: CRC Press
Release Date : 2017-04-07
Essentials Of Nonlinear Circuit Dynamics With Matlab And Laboratory Experiments written by Arturo Buscarino and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-07 with Technology & Engineering categories.
This book deals with nonlinear dynamics of electronic circuits, which could be used in robot control, secure communications, sensors and synchronized networks. The genesis of the content is related to a course on complex adaptive systems that has been held at the University of Catania since 2005. The efforts are devoted in order to emulate with nonlinear electronic circuits nonlinear dynamics. Step-by-step methods show the essential concepts of complex systems by using the Varela diagrams and accompanying MATLAB® exercises to reinforce new information. Special attention has been devoted to chaotic systems and networks of chaotic circuits by exploring the fundamentals, such as synchronization and control. The aim of the book is to give to readers a comprehensive view of the main concepts of nonlinear dynamics to help them better understand complex systems and their control through the use of electronics devices.
Chaos For Engineers
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Author : Tomasz Kapitaniak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Chaos For Engineers written by Tomasz Kapitaniak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Chaos occurs widely in both natural and man-made systems. Recently, examples of the potential usefulness of chaotic behavior have caused growing interest among engineers and applied scientists. In this book the new mathematical ideas in nonlinear dynamics are described in such a way that engineers can apply them to real physical systems. From a review of the first edition by Prof. El Naschie, University of Cambridge: "Small is beautiful and not only that, it is comprehensive as well. These are the spontaneous thoughts which came to my mind after browsing in this latest book by Prof. Thomas Kapitaniak, probably one of the most outstanding scientists working on engineering applications of Nonlinear Dynamics and Chaos today. A more careful reading reinforced this first impression....The presentation is lucid and user friendly with theory, examples, and exercises."
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1991
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mechanics, Applied categories.