Chaotic Numerics

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Practical Numerical Algorithms for Chaotic Systems

Author : Thomas S. Parker
Publisher : Springer Science & Business Media
ISBN 13 : 1461234867
Total Pages : 354 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Practical Numerical Algorithms for Chaotic Systems by : Thomas S. Parker

Download or read book Practical Numerical Algorithms for Chaotic Systems written by Thomas S. Parker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaos and Fractals

Author : David P. Feldman
Publisher : Oxford University Press
ISBN 13 : 0199566437
Total Pages : 431 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Chaos and Fractals by : David P. Feldman

Download or read book Chaos and Fractals written by David P. Feldman and published by Oxford University Press. This book was released on 2012-08-09 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

Chaotic Systems

Author : Esteban Tlelo-Cuautle
Publisher : BoD – Books on Demand
ISBN 13 : 9533075643
Total Pages : 326 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Chaotic Systems by : Esteban Tlelo-Cuautle

Download or read book Chaotic Systems written by Esteban Tlelo-Cuautle and published by BoD – Books on Demand. This book was released on 2011-02-14 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of major developments in chaos systems covering aspects on chaotic behavioral modeling and simulation, control and synchronization of chaos systems, and applications like secure communications. It is a good source to acquire recent knowledge and ideas for future research on chaos systems and to develop experiments applied to real life problems. That way, this book is very interesting for students, academia and industry since the collected chapters provide a rich cocktail while balancing theory and applications.

Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization

Author : Esteban Tlelo-Cuautle
Publisher : CRC Press
ISBN 13 : 100034665X
Total Pages : 267 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization by : Esteban Tlelo-Cuautle

Download or read book Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization written by Esteban Tlelo-Cuautle and published by CRC Press. This book was released on 2021-05-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have devised different chaotic systems that are modeled by integer or fractional-order differential equations, and whose mathematical models can generate chaos or hyperchaos. The numerical methods to simulate those integer and fractional-order chaotic systems are quite different and their exactness is responsible in the evaluation of characteristics like Lyapunov exponents, Kaplan-Yorke dimension, and entropy. One challenge is estimating the step-size to run a numerical method. It can be done analyzing the eigenvalues of self-excited attractors, while for hidden attractors it is difficult to evaluate the equilibrium points that are required to formulate the Jacobian matrices. Time simulation of fractional-order chaotic oscillators also requires estimating a memory length to achieve exact results, and it is associated to memories in hardware design. In this manner, simulating chaotic/hyperchaotic oscillators of integer/fractional-order and with self-excited/hidden attractors is quite important to evaluate their Lyapunov exponents, Kaplan-Yorke dimension and entropy. Further, to improve the dynamics of the oscillators, their main characteristics can be optimized applying metaheuristics, which basically consists of varying the values of the coefficients of a mathematical model. The optimized models can then be implemented using commercially available amplifiers, field-programmable analog arrays (FPAA), field-programmable gate arrays (FPGA), microcontrollers, graphic processing units, and even using nanometer technology of integrated circuits. The book describes the application of different numerical methods to simulate integer/fractional-order chaotic systems. These methods are used within optimization loops to maximize positive Lyapunov exponents, Kaplan-Yorke dimension, and entropy. Single and multi-objective optimization approaches applying metaheuristics are described, as well as their tuning techniques to generate feasible solutions that are suitable for electronic implementation. The book details several applications of chaotic oscillators such as in random bit/number generators, cryptography, secure communications, robotics, and Internet of Things.

Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday

Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814434876
Total Pages : 362 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday by : Christophe Letellier

Download or read book Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday written by Christophe Letellier and published by World Scientific. This book was released on 2013-01-11 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

Exploring Chaos

Author : Brian Davies
Publisher : CRC Press
ISBN 13 : 0429982496
Total Pages : 200 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Exploring Chaos by : Brian Davies

Download or read book Exploring Chaos written by Brian Davies and published by CRC Press. This book was released on 2018-05-04 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. It describes the theory of fractals, focusing on the importance of scaling and ordinary differential equations.

Chaos in Automatic Control

Author : Wilfrid Perruquetti
Publisher : CRC Press
ISBN 13 : 1351836811
Total Pages : 398 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Chaos in Automatic Control by : Wilfrid Perruquetti

Download or read book Chaos in Automatic Control written by Wilfrid Perruquetti and published by CRC Press. This book was released on 2018-10-03 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic behavior arises in a variety of control settings. In some cases, it is beneficial to remove this behavior; in others, introducing or taking advantage of the existing chaotic components can be useful for example in cryptography. Chaos in Automatic Control surveys the latest methods for inserting, taking advantage of, or removing chaos in a variety of applications. This book supplies the theoretical and pedagogical basis of chaos in control systems along with new concepts and recent developments in the field. Presented in three parts, the book examines open-loop analysis, closed-loop control, and applications of chaos in control systems. The first section builds a background in the mathematics of ordinary differential and difference equations on which the remainder of the book is based. It includes an introductory chapter by Christian Mira, a pioneer in chaos research. The next section explores solutions to problems arising in observation and control of closed-loop chaotic control systems. These include model-independent control methods, strategies such as H-infinity and sliding modes, polytopic observers, normal forms using homogeneous transformations, and observability normal forms. The final section explores applications in wireless transmission, optics, power electronics, and cryptography. Chaos in Automatic Control distills the latest thinking in chaos while relating it to the most recent developments and applications in control. It serves as a platform for developing more robust, autonomous, intelligent, and adaptive systems.

Numerical Analysis: A R Mitchell 75th Birthday Volume

Author : D F Griffiths
Publisher : World Scientific
ISBN 13 : 9814498785
Total Pages : 381 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Numerical Analysis: A R Mitchell 75th Birthday Volume by : D F Griffiths

Download or read book Numerical Analysis: A R Mitchell 75th Birthday Volume written by D F Griffiths and published by World Scientific. This book was released on 1996-05-15 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis.

Chaos, Cnn, Memristors And Beyond: A Festschrift For Leon Chua (With Dvd-rom, Composed By Eleonora Bilotta)

Author : Andrew Adamatzky
Publisher : World Scientific
ISBN 13 : 9814434817
Total Pages : 562 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Chaos, Cnn, Memristors And Beyond: A Festschrift For Leon Chua (With Dvd-rom, Composed By Eleonora Bilotta) by : Andrew Adamatzky

Download or read book Chaos, Cnn, Memristors And Beyond: A Festschrift For Leon Chua (With Dvd-rom, Composed By Eleonora Bilotta) written by Andrew Adamatzky and published by World Scientific. This book was released on 2013-01-02 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first — cellular nonlinear networks, nonlinear circuits and cellular automata — deals with Chua's Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua's circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua's views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into ‘ancient memristors’, analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book.The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science.The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua's circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike.

A Philosophical Analysis of Chaos Theory

Author : Lena C. Zuchowski
Publisher : Springer
ISBN 13 : 3319546635
Total Pages : 149 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis A Philosophical Analysis of Chaos Theory by : Lena C. Zuchowski

Download or read book A Philosophical Analysis of Chaos Theory written by Lena C. Zuchowski and published by Springer. This book was released on 2017-05-03 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an analysis of the construction, diagnosis (as chaotic) and evaluation of models in chaos theory. It contains a detailed look at the interaction of the different models used in chaos theory and analyses how these models influence the way chaos is defined. Furthermore, the book discusses the conditions for the occurrence of chaos and the detection of chaos in nature.

Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 981122191X
Total Pages : 561 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Recent Trends In Chaotic, Nonlinear And Complex Dynamics by : Jan Awrejcewicz

Download or read book Recent Trends In Chaotic, Nonlinear And Complex Dynamics written by Jan Awrejcewicz and published by World Scientific. This book was released on 2021-07-26 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

The Theory of Chaotic Attractors

Author : Brian R. Hunt
Publisher : Springer Science & Business Media
ISBN 13 : 9780387403496
Total Pages : 528 pages
Book Rating : 4.4/5 (34 download)

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Book Synopsis The Theory of Chaotic Attractors by : Brian R. Hunt

Download or read book The Theory of Chaotic Attractors written by Brian R. Hunt and published by Springer Science & Business Media. This book was released on 2004-01-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.

Controlling Chaos

Author : Huaguang Zhang
Publisher : Springer Science & Business Media
ISBN 13 : 1848825234
Total Pages : 357 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Controlling Chaos by : Huaguang Zhang

Download or read book Controlling Chaos written by Huaguang Zhang and published by Springer Science & Business Media. This book was released on 2009-06-18 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Controlling Chaos achieves three goals: the suppression, synchronisation and generation of chaos, each of which is the focus of a separate part of the book. The text deals with the well-known Lorenz, Rössler and Hénon attractors and the Chua circuit and with less celebrated novel systems. Modelling of chaos is accomplished using difference equations and ordinary and time-delayed differential equations. The methods directed at controlling chaos benefit from the influence of advanced nonlinear control theory: inverse optimal control is used for stabilization; exact linearization for synchronization; and impulsive control for chaotification. Notably, a fusion of chaos and fuzzy systems theories is employed. Time-delayed systems are also studied. The results presented are general for a broad class of chaotic systems. This monograph is self-contained with introductory material providing a review of the history of chaos control and the necessary mathematical preliminaries for working with dynamical systems.

Chaos

Author : Richard Kautz
Publisher : Oxford University Press
ISBN 13 : 0199594570
Total Pages : 384 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Chaos by : Richard Kautz

Download or read book Chaos written by Richard Kautz and published by Oxford University Press. This book was released on 2011 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: One CD-ROM disc in pocket.

Chaos In Circuits And Systems

Author : Guanrong Chen
Publisher : World Scientific
ISBN 13 : 9814488704
Total Pages : 656 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Chaos In Circuits And Systems by : Guanrong Chen

Download or read book Chaos In Circuits And Systems written by Guanrong Chen and published by World Scientific. This book was released on 2002-06-03 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.

Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption

Author : Banerjee, Santo
Publisher : IGI Global
ISBN 13 : 1615207384
Total Pages : 596 pages
Book Rating : 4.6/5 (152 download)

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Book Synopsis Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption by : Banerjee, Santo

Download or read book Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption written by Banerjee, Santo and published by IGI Global. This book was released on 2010-07-31 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few decades, there has been numerous research studies conducted involving the synchronization of dynamical systems with several theoretical studies and laboratory experimentations demonstrating the pivotal role for this phenomenon in secure communications. Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption explores the combination of ordinary and time delayed systems and their applications in cryptographic encoding. This innovative publication presents a critical mass of the most sought after research, providing relevant theoretical frameworks and the latest empirical research findings in this area of study.

Applied Symbolic Dynamics And Chaos

Author : Bailin Hao
Publisher : World Scientific
ISBN 13 : 9814495972
Total Pages : 460 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Applied Symbolic Dynamics And Chaos by : Bailin Hao

Download or read book Applied Symbolic Dynamics And Chaos written by Bailin Hao and published by World Scientific. This book was released on 1998-07-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.