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Linear Chaos
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Author :Karl-G. Grosse-Erdmann Publisher :Springer Science & Business Media ISBN 13 :1447121708 Total Pages :388 pages Book Rating :4.4/5 (471 download)
Book Synopsis Linear Chaos by : Karl-G. Grosse-Erdmann
Download or read book Linear Chaos written by Karl-G. Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis Differential Equations, Dynamical Systems, and an Introduction to Chaos by : Morris W. Hirsch
Download or read book Differential Equations, Dynamical Systems, and an Introduction to Chaos written by Morris W. Hirsch and published by Academic Press. This book was released on 2004 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Book Synopsis Analysis of Chaotic Behavior in Non-linear Dynamical Systems by : Michał Piórek
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 132 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.
Download or read book Chaos written by Kathleen Alligood and published by Springer. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
Book Synopsis Nonlinear Dynamics and Quantum Chaos by : Sandro Wimberger
Download or read book Nonlinear Dynamics and Quantum Chaos written by Sandro Wimberger and published by Springer. This book was released on 2014-05-13 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Book Synopsis Chaos, Complexity and Leadership 2020 by : Şefika Şule Erçetin
Download or read book Chaos, Complexity and Leadership 2020 written by Şefika Şule Erçetin and published by Springer Nature. This book was released on 2021-07-30 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in different fields of the sciences and leadership. In addition, it explores chaotic and complex systems from all fields of knowledge in order to stake a claim of prevalence of compatibility between knowledge fields. Particular emphasis is placed on exploring non-linearity in order to open a discussion on new approaches to and perspectives on chaos, complexity and leadership. Readers will find coverage of important events that have recently taken place in our world, regardless of whether they were social, political, economic or scientific in nature. The book explores diverse aspects of and issues related to the effects of chaos and complexity in the world; discusses the application of nonlinear dynamics in order to arrive at transformational policies; and offers projections of tomorrow’s world using an interdisciplinary approach. Though primarily intended for readers with an interest in nonlinear science, thanks to its focus on the application of chaos and complexity to other disciplines, the book appeals to a broad readership.
Book Synopsis Clinical Chaos by : Linda Chamberlain
Download or read book Clinical Chaos written by Linda Chamberlain and published by Routledge. This book was released on 2016-01-28 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Psychology and the social sciences are in need of a new foundation, one that provides a better model for understanding complex behavior. Chaos theory and its newest permutation, complexity theory, offers an innovative, exciting and potentially revolutionary leap forward in the evolution of scientific thought. In Clinical Chaos, therapists and theoreticians from various areas in the social sciences will explore the relevance and implications for non-linear dynamics in observing, explaining, and understanding human behavior. At last, the scientific search can again encompass surprise, transformation, unpredictability, and pattern. This book is intended to introduce social scientists to chaos through paths that are already familiar. By linking chaos theory with existing psychological theories and established areas of clinical pursuit, Clinical Chaos emphasizes the relevance of this new science in providing a more flexible useful model for complexities of life.
Book Synopsis Chaos and Information Processing by : John Nicolis
Download or read book Chaos and Information Processing written by John Nicolis and published by World Scientific. This book was released on 1991 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first attempt to give a chaotic dynamics interpretation of processes having to do with category formation and pattern recognition by systems possessing simple hardware e.g. few degrees of freedom. It is multidisciplinary in its approach and would be useful to readers from various fields.
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.
Book Synopsis Order and Chaos in Dynamical Astronomy by : George Contopoulos
Download or read book Order and Chaos in Dynamical Astronomy written by George Contopoulos and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.
Book Synopsis Chaos, CNN, Memristors and Beyond by : Andrew Adamatzky
Download or read book Chaos, CNN, Memristors and Beyond written by Andrew Adamatzky and published by World Scientific. This book was released on 2013-01-02 with total page 564 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. Contents:Cellular Nonlinear Networks, Nonlinear Circuits and Cellular Automata:Genealogy of Chua's Circuit (Peter Kennedy)Impasse Points, Mutators, and Other Chua Creations (Hyongsuk Kim)Chua's Lagrangian Circuit Elements (Orla Feely)From CNN Dynamics to Cellular Wave Computers (Tamas Roska)Contributions of CNN to Bio-Robotics and Brain Science (Paolo Arena and Luca Patané)From Radio-amateurs' Electronics to Toroidal Chaos (Otto E Rössler and Christophe Letellier)Analyzing the Dynamics of Excitatory Neural Networks by Synaptic Cellular Automata (V Nekorkin, A Dmitrichev, D Kasatkin and V Afraimovich)Dynamical Systems Perspective of Wolfram's Cellular Automata (M Courbage and B Kamińki)The Genesis of Chua's Circuit: Connecting Science, Art and Creativity (Francesca Bertacchini, Eleonora Bilotta, Giuseppe Laria and Pietro Pantano)Nonlinear Electronics Laboratory (NOEL): A Reminiscence (Chai Wah Wu)Bursting in Cellular Automata and Cardiac Arrhythmias (Gil Bub, Alvin Shrier and Leon Glass)Local Activity Principle: The Cause of Complexity and Symmetry Breaking (Klaus Mainzer)Explorations in the Forest of Bifurcation Trees: Route from Chua's Circuit to Chua's Memristive Oscillator (Łukasz Czerwiński and Maciej J Ogorzałek)Chua's Nonlinear Dynamics Perspective Cellular Automata (Giovanni E Pazienza)Application of CNN to Brainlike Computing (Bertram E Shi)Ideal Turbulence Phenomenon and Transmission Line with Chua's Diode (E Yu Romanenko and A N Sharkovsky)Chaos in Electronic Circuits: Chua's Contribution (1980–2000) (Christophe Letellier)Dynamical Systems and Chaos:Connectivity of Julia Sets for Singularly Perturbed Rational Maps (Robert L Devaney and Elizabeth D Russell)Structural Transformations and Stability of Dynamical Networks (L A Bunimovich and B Z Webb)Chua's Time (Arturo Buscarino, Luigi Fortuna and Mattia Frasca)Chaotic Neural Networks and Beyond (Kazuyuki Aihara, Taiji Yamada and Makito Oku)Chaotic Neocritical Dynamics (Walter J Freeman)Nonlinear Dynamics of a Class of Piecewise Linear Systems (M Lakshmanan and K Murali)Chaotic Mathematical Circuitry (R Lozi)Chua's Equation was Proved to be Chaotic in Two Years, Lorenz Equation in Thirty Six Years (Bharathwaj Muthuswamy)Toward a Quantitative Formulation of Emergence (G Nicolis)Controlled Synchronization of Chaotic Oscillators with Huygens' Coupling (J Peńa-Ramírez, R H B Fey and H Nijmeijer)Using Time-Delay Feedback for Control and Synchronization of Dynamical Systems (Kestutis Pyragas, Viktoras Pyragas and Tatjana Pyragiene)Models of Catastrophic Events and Suggestions to Foretell Them (Yves Pomeau and Martine Le Berre)Synchronization Propensity in Networks of Dynamical Systems: A Purely Topological Indicator (Stefano Fasani and Sergio Rinaldi)Further Progress in Partial Control of Chaotic Systems (Juan Sabuco, Miguel Sanjuan and Samuel Zambrano)Phase and Complete Synchronizations in Time-Delay Systems (D V Senthilkumar, M Manju Shrii and J Kurths)Symbolic Dynamics and Spiral Structures due to the Saddle-Focus Bifurcations (Andrey Shilnikov, Leonid Shilnikov and Roberto Barrio)Dynamics of Periodically Forced Mass Point on Constrained Surface with Changing Curvature (Yoshisuke Ueda)Solitons for Describing 3-D Physical Reality: The Current Frontier (Paul J Werbos)Thermal Solitons in 1D and 2D Anharmonic Lattices — Solectrons and the Organization of Non-Linear Fluctuations in Long-Living Dynamical Structures (M G Velarde, W Ebeling and A P Chetverikov)Global Optimizations by Intermittent Diffusion (Shui-Nee Chow, Tzi-Sheng Yang and Hao-Min Zhou)Memristors:How We Found the Missing Memristor (R Stanley Williams)Aftermath of Finding the Memristor (R Stanley Williams)The Singing Arc: The Oldest Memristor? (Jean-Marc Ginoux and Bruno Rossetto)Two Centuries of Memristors (Themistoklis Prodromakis)State Equations for Active Circuits with Memristors (Martin Hasler)Analytical Analysis of Memristive Networks (Torsten Schmidt, Willi Neudeck, Ute Feldmann and Ronald Tetzlaff)Hardware Memristor Emulators (Andrew L Fitch, Herbert H C Iu and Chi K Tse)Leon Chua's Memristor (Guanrong Chen) Readership: Graduate students, researchers and academics in all engineering disciplines as well as historians of science. Keywords:Memristors;CNN;Chaos;Dynamical SystemsKey Features:Unique personality of Leon Chua and enormity of his achievements underpins the structure of the bookConglomerate of hot topics: memristors, chaos, computationalOriginal papers from renown scholars and researchers as well as numerous tutorials and historical expositions on each of the topicsHigh pedagogical value makes the book a timeless referenceReviews: "It is a veritable kaleidoscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike." Zentralblatt MATH
Download or read book Chaos Control written by Guanrong Chen and published by Springer Science & Business Media. This book was released on 2003-07-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.
Book Synopsis Chaos and Statistical Methods by : Y. Kuramoto
Download or read book Chaos and Statistical Methods written by Y. Kuramoto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 6th Kyoto Summer Institute devoted to "Chaos and Statistical Mechanics" was held from September 12 to 15, 1983, at the Research Institute forMathematical Sciences, Kyoto University, and at Hotel Kuniso. The meeting was aimed at clari fying various aspects of chaotic systems appearing in different scientific disci pl ines, critically examining related mathematical methods developed so far, thus preparing for possible breakthroughs, among others, for the opening of a new period of statistical mechanics of deterministic systems. The number of partici pants was 135,of which 24 were from abroad. We believe that the well-prepared lecture of each speaker and lively discussions among many participants from various research fields led the meeting to a successful conclusion. The 6th KSI was organized by the Research Institute for Fundamental Physics. A number of young chaos researchers in Japan also participated actively in the organization. We were also in close contact with the organizer of the IUTAM Sym posium on "Turbulence and Chaotic Phenomena in Fluids" (Kyoto Kaikan Conference Hall, Kyoto, September 5-10 1983). This volume contains most of the lectures presented at the 6th KSI. We are very grateful to all the authors for their efforts in preparing such excellent manuscripts. The 6th KSI was supported by the Ministry of Education, Science and Culture and the Yamada Science Foundation. The organizing committee acknowledges gratefully their generous financial support. Finally, than'ks are due to Dr. M. Toya and Miss T. Sumide for their invaluable assistance.
Book Synopsis Chaotic Signals in Digital Communications by : Marcio Eisencraft
Download or read book Chaotic Signals in Digital Communications written by Marcio Eisencraft and published by CRC Press. This book was released on 2018-09-03 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such systems. A Combination of Tutorials and In-Depth, Cutting-Edge Research Featuring contributions by active leading researchers, the book begins with an introduction to communication theory, dynamical systems, and chaotic communications suitable for those new to the field. This lays a solid foundation for the more applied chapters that follow. A Toolbox of Techniques—Including New Ways to Tackle Channel Imperfections The book covers typical chaos communication methods, namely chaotic masking, chaotic modulation, chaotic shift key, and symbolic message bearing, as well as bidirectional communication and secure communication. It also presents novel methodologies to deal with communication channel imperfections. These tackle band-limited channel chaos communication, radio channels with fading, and the resistance of a special chaotic signal to multipath propagations. In addition, the book addresses topics related to engineering applications, such as optical communications, chaotic matched filters and circuit implementations, and microwave frequency-modulated differential chaos shift keying (FM-DCSK) systems. Insights for Both Theoretical and Experimental Researchers Combining theory and practice, this book offers a unique perspective on chaotic communication in the context of non-ideal conditions. Written for theoretical and experimental researchers, it tackles the practical issues faced in implementing chaos-based signals and systems in digital communications applications.
Book Synopsis Chaos and Non-linear Models in Economics by : John Creedy
Download or read book Chaos and Non-linear Models in Economics written by John Creedy and published by Edward Elgar Publishing. This book was released on 1994 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear models are increasingly being applied to phenomena that are otherwise very difficult to model such as financial markets, economic growth, agricultural price cycles, business cycles, diffusion processes and overlapping generation models. Chaos and Non-Linear Models in Economics makes important advances in the theory and application of non-linear modelling accessible to advanced students. The contributions to this volume include both introductory chapters which review the fundamental theoretical and statistical characteristics of non-linear models - and keep the use of mathematics to a minimum - and chapters which introduce more sophisticated techniques.
