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Author : Gérard Iooss
Publisher : North-Holland
ISBN 13 :
Total Pages : 752 pages
Book Rating : 4.3/5 (91 download)
Download or read book Chaotic Behaviour of Deterministic Systems written by Gérard Iooss and published by North-Holland. This book was released on 1983 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert L. Devaney
Publisher : CRC Press
ISBN 13 : 100048677X
Total Pages : 571 pages
Book Rating : 4.0/5 (4 download)
Download or read book An Introduction To Chaotic Dynamical Systems written by Robert L. Devaney and published by CRC Press. This book was released on 2021-11-28 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics. Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field. This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory. The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field is becoming more and more important in a variety of scientific disciplines. New to this edition: •Greatly expanded coverage complex dynamics now in Chapter 2 •The third chapter is now devoted to higher dimensional dynamical systems. •Chapters 2 and 3 are independent of one another. •New exercises have been added throughout.
Author : Milos Marek
Publisher : Cambridge University Press
ISBN 13 : 9780521438308
Total Pages : 384 pages
Book Rating : 4.4/5 (383 download)
Download or read book Chaotic Behaviour of Deterministic Dissipative Systems written by Milos Marek and published by Cambridge University Press. This book was released on 1995-07-20 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.
Author : Aleksand Janicki
Publisher : CRC Press
ISBN 13 : 1000447804
Total Pages : 378 pages
Book Rating : 4.0/5 (4 download)
Download or read book Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes written by Aleksand Janicki and published by CRC Press. This book was released on 2021-07-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents new computer methods in approximation, simulation, and visualization for a host of alpha-stable stochastic processes.
Author : Gregory L. Baker
Publisher : Cambridge University Press
ISBN 13 : 9780521471060
Total Pages : 282 pages
Book Rating : 4.4/5 (71 download)
Download or read book Chaotic Dynamics written by Gregory L. Baker and published by Cambridge University Press. This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Author : H.-O. Peitgen
Publisher : Springer
ISBN 13 : 3540351299
Total Pages : 513 pages
Book Rating : 4.5/5 (43 download)
Download or read book Functional Differential Equations and Approximation of Fixed Points written by H.-O. Peitgen and published by Springer. This book was released on 2006-11-15 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to Heinz Unger on occasion of his 65. birthday
Author : Tomasz Kapitaniak
Publisher : World Scientific
ISBN 13 : 9789810204105
Total Pages : 256 pages
Book Rating : 4.2/5 (41 download)
Download or read book Chaos in Systems with Noise written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1990 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.
Author : Robert L. L. Devaney
Publisher : CRC Press
ISBN 13 : 1000065650
Total Pages : 318 pages
Book Rating : 4.0/5 ( download)
Download or read book A First Course In Chaotic Dynamical Systems written by Robert L. L. Devaney and published by CRC Press. This book was released on 2020-04-21 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses. Features More extensive coverage of fractals, including objects like the Sierpinski carpet and others that appear as Julia sets in the later sections on complex dynamics, as well as an actual chaos "game." More detailed coverage of complex dynamical systems like the quadratic family and the exponential maps. New sections on other complex dynamical systems like rational maps. A number of new and expanded computer experiments for students to perform. About the Author Robert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.
Author : Ali Sanayei
Publisher : Springer
ISBN 13 : 3319067818
Total Pages : 277 pages
Book Rating : 4.3/5 (19 download)
Download or read book Chaotic Harmony written by Ali Sanayei and published by Springer. This book was released on 2014-06-11 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating book written by Ali Sanayei and Otto E. Rössler is not a classic scientific publication, but a vivid dialogue on science, philosophy and the interdisciplinary intersections of science and technology with biographic elements. Chaotic Harmony: A Dialog about Physics, Complexity and Life represents a discussion between Otto Rössler and his colleague and student, focusing on the different areas of science and highlights their mutual relations. The book's concept of interdisciplinary dialogue is unusual nowadays although it has a long tradition in science. It provides insight not only into interesting topics that are often closely linked, but also into the mind of a prominent scientist in the field of physics, chaos and complexity in general. It allows a deep look into the fascinating process of scientific development and discovery and provides a very interesting background of known and unknown facts in the areas of complex processes in physics, cosmology, biology, brains and systems in general. This book will be valuable to all who are interested in science, its evolution and in an unconventional and original look at various issues. Surely it can serve as an inspiration for students, explaining the often overlooked fact that science and philosophy enrich each other.
Author : Yurii Bolotin
Publisher : Springer
ISBN 13 : 3319424963
Total Pages : 286 pages
Book Rating : 4.3/5 (194 download)
Download or read book Chaos: Concepts, Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Author : Tomasz Kapitaniak
Publisher : World Scientific
ISBN 13 : 9789810206536
Total Pages : 672 pages
Book Rating : 4.2/5 (65 download)
Download or read book Chaotic Oscillators written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1992 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Author : Henry Abarbanel
Publisher : Springer Science & Business Media
ISBN 13 : 1461207630
Total Pages : 278 pages
Book Rating : 4.4/5 (612 download)
Download or read book Analysis of Observed Chaotic Data written by Henry Abarbanel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.
Author : Jacques M. Bahi
Publisher : CRC Press
ISBN 13 : 1466554509
Total Pages : 236 pages
Book Rating : 4.4/5 (665 download)
Download or read book Discrete Dynamical Systems and Chaotic Machines written by Jacques M. Bahi and published by CRC Press. This book was released on 2013-06-07 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science. Covering both theoretical and practical aspects, the book presents: Key mathematical and physical ideas in chaos theory Computer science fundamentals, clearly establishing that chaos properties can be satisfied by finite state machines Concrete applications of chaotic machines in computer security, including pseudorandom number generators, hash functions, digital watermarking, and steganography Concrete applications of chaotic machines in wireless sensor networks, including secure data aggregation and video surveillance Until the authors’ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book illustrates how chaos theory enables the study of computer security problems, such as steganalysis, that otherwise could not be tackled. It also explains how the theory reinforces existing cryptographically secure tools and schemes.
Author : Wilfrid Perruquetti
Publisher : CRC Press
ISBN 13 : 1420027859
Total Pages : 592 pages
Book Rating : 4.4/5 (2 download)
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 592 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.
Author : Brian Davies
Publisher : Westview Press
ISBN 13 : 0786745614
Total Pages : 258 pages
Book Rating : 4.7/5 (867 download)
Download or read book Exploring Chaos written by Brian Davies and published by Westview Press. This book was released on 2009-02-23 with total page 258 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. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below). The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincaré sections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software.
Author : Charilaos Skiadas
Publisher : World Scientific
ISBN 13 : 9814271330
Total Pages : 435 pages
Book Rating : 4.8/5 (142 download)
Download or read book Topics on Chaotic Systems written by Charilaos Skiadas and published by World Scientific. This book was released on 2009 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.
Author : Michał Piórek
Publisher : Springer
ISBN 13 : 3319948873
Total Pages : 136 pages
Book Rating : 4.3/5 (199 download)
Download or read book Analysis of Chaotic Behavior in Non-linear Dynamical Systems written by Michał Piórek and published by Springer. This book was released on 2018-07-12 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All methods and algorithms are designed to allow detection of deterministic chaos behavior in quaternion data representing the rotation of a body in 3D space. This book is an excellent reference for engineers, researchers, and postgraduate students conducting research on human gait analysis, healthcare informatics, dynamical systems with deterministic chaos or time series analysis.
