Search Results for "elegant-chaos-algebraically-simple-chaotic-flows"

Elegant Chaos

Elegant Chaos

Algebraically Simple Chaotic Flows

  • Author: Julien C. Sprott
  • Publisher: World Scientific
  • ISBN: 9812838821
  • Category: Mathematics
  • Page: 304
  • View: 2346
DOWNLOAD NOW »
This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rossler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos.The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.

Systems with Hidden Attractors

Systems with Hidden Attractors

From Theory to Realization in Circuits

  • Author: Viet-Thanh Pham,Christos Volos,Tomasz Kapitaniak
  • Publisher: Springer
  • ISBN: 3319537210
  • Category: Technology & Engineering
  • Page: 105
  • View: 7170
DOWNLOAD NOW »
This brief provides a general overview of nonlinear systems that exhibit hidden-attractor behavior, a topic of interest in subjects as divers as physics, mechanics, electronics and secure communications. The brief is intended for readers who want to understand the concepts of the hidden attractor and hidden-attractor systems and to implement such systems experimentally using common electronic components. Emergent topics in circuit implementation of systems with hidden attractors are included. The brief serves as an up-to-date reference on an important research topic for undergraduate/graduate students, laboratory researchers and lecturers in various areas of engineering and physics.

Advances in Chaos Theory and Intelligent Control

Advances in Chaos Theory and Intelligent Control

  • Author: Ahmad Taher Azar,Sundarapandian Vaidyanathan
  • Publisher: Springer
  • ISBN: 3319303406
  • Category: Computers
  • Page: 873
  • View: 6619
DOWNLOAD NOW »
The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate students, researchers, and practitioners in the areas of chaos theory and intelligent control.

Fractional Dynamics

Fractional Dynamics

  • Author: Carlo Cattani,Hari M. Srivastava,Xiao-Jun Yang
  • Publisher: Walter de Gruyter GmbH & Co KG
  • ISBN: 3110472090
  • Category: Mathematics
  • Page: 392
  • View: 6020
DOWNLOAD NOW »
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics.

Elegant Fractals

Elegant Fractals

Automated Generation of Computer Art

  • Author: Julien Clinton Sprott
  • Publisher: N.A
  • ISBN: 9789813237131
  • Category:
  • Page: N.A
  • View: 1761
DOWNLOAD NOW »

Advances and Applications in Chaotic Systems

Advances and Applications in Chaotic Systems

  • Author: Sundarapandian Vaidyanathan,Christos Volos
  • Publisher: Springer
  • ISBN: 3319302795
  • Category: Technology & Engineering
  • Page: 600
  • View: 2226
DOWNLOAD NOW »
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

The Topology of Chaos

The Topology of Chaos

Alice in Stretch and Squeezeland

  • Author: Robert Gilmore,Marc Lefranc
  • Publisher: John Wiley & Sons
  • ISBN: 352763942X
  • Category: Mathematics
  • Page: 618
  • View: 6193
DOWNLOAD NOW »
A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical systems. Since its publication in 2002, important theoretical and experimental advances have put the topological analysis program on a firmer basis. This second edition includes relevant results and connects the material to other recent developments. Following significant improvements will be included: * A gentler introduction to the topological analysis of chaotic systems for the non expert which introduces the problems and questions that one commonly encounters when observing a chaotic dynamics and which are well addressed by a topological approach: existence of unstable periodic orbits, bifurcation sequences, multistability etc. * A new chapter is devoted to bounding tori which are essential for achieving generality as well as for understanding the influence of boundary conditions. * The new edition also reflects the progress which had been made towards extending topological analysis to higher-dimensional systems by proposing a new formalism where evolving triangulations replace braids. * There has also been much progress in the understanding of what is a good representation of a chaotic system, and therefore a new chapter is devoted to embeddings. * The chapter on topological analysis program will be expanded to cover traditional measures of chaos. This will help to connect those readers who are familiar with those measures and tests to the more sophisticated methodologies discussed in detail in this book. * The addition of the Appendix with both frequently asked and open questions with answers gathers the most essential points readers should keep in mind and guides to corresponding sections in the book. This will be of great help to those who want to selectively dive into the book and its treatments rather than reading it cover to cover. What makes this book special is its attempt to classify real physical systems (e.g. lasers) using topological techniques applied to real date (e.g. time series). Hence it has become the experimenter?s guidebook to reliable and sophisticated studies of experimental data for comparison with candidate relevant theoretical models, inevitable to physicists, mathematicians, and engineers studying low-dimensional chaotic systems.

Instabilities, Chaos and Turbulence

Instabilities, Chaos and Turbulence

  • Author: Paul Manneville
  • Publisher: World Scientific
  • ISBN: 1848163924
  • Category: Science
  • Page: 439
  • View: 8620
DOWNLOAD NOW »
This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Fractional-Order Nonlinear Systems

Fractional-Order Nonlinear Systems

Modeling, Analysis and Simulation

  • Author: Ivo Petras
  • Publisher: Springer Science & Business Media
  • ISBN: 3642181015
  • Category: Technology & Engineering
  • Page: 218
  • View: 2775
DOWNLOAD NOW »
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors

Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors

  • Author: Viet-Thanh Pham,Sundarapandian Vaidyanathan,Christos Volos,Tomasz Kapitaniak
  • Publisher: Springer
  • ISBN: 3319712438
  • Category: Computers
  • Page: 497
  • View: 9124
DOWNLOAD NOW »
This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.

An Introduction to Mechanics

An Introduction to Mechanics

  • Author: Daniel Kleppner,Robert Kolenkow
  • Publisher: Cambridge University Press
  • ISBN: 0521198119
  • Category: Science
  • Page: 566
  • View: 7151
DOWNLOAD NOW »
This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.

Chaos and Time-series Analysis

Chaos and Time-series Analysis

  • Author: Julien C. Sprott
  • Publisher: Peterson's
  • ISBN: 9780198508403
  • Category: Mathematics
  • Page: 507
  • View: 6958
DOWNLOAD NOW »
This book provides a broad coverage and has acessible style of exposition. Emphasis is on physical concepts and useful results, rather than rigorous mathematical proofs. Completeing this volume is free and user-friendly software.

Fractional Order Control and Synchronization of Chaotic Systems

Fractional Order Control and Synchronization of Chaotic Systems

  • Author: Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas
  • Publisher: Springer
  • ISBN: 3319502492
  • Category: Computers
  • Page: 877
  • View: 5627
DOWNLOAD NOW »
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional control and stability, the book also discusses key applications of fractional order chaotic systems, as well as multidisciplinary solutions developed via control modeling. As such, it offers the perfect reference guide for graduate students, researchers and practitioners in the areas of fractional order control systems and fractional order chaotic systems.

Chaos Theory Tamed

Chaos Theory Tamed

  • Author: Garnett Williams
  • Publisher: CRC Press
  • ISBN: 1482295415
  • Category: Science
  • Page: 520
  • View: 6363
DOWNLOAD NOW »
This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents. Only basic algebra, trigonometry, geometry and statistics are assumed as background. The author focuses on the most important topics, very much with the general scientist in mind.

Python Programming

Python Programming

An Introduction to Computer Science

  • Author: John M. Zelle
  • Publisher: Franklin, Beedle & Associates, Inc.
  • ISBN: 1887902996
  • Category: Computers
  • Page: 517
  • View: 4580
DOWNLOAD NOW »
This book is suitable for use in a university-level first course in computing (CS1), as well as the increasingly popular course known as CS0. It is difficult for many students to master basic concepts in computer science and programming. A large portion of the confusion can be blamed on the complexity of the tools and materials that are traditionally used to teach CS1 and CS2. This textbook was written with a single overarching goal: to present the core concepts of computer science as simply as possible without being simplistic.

Modeling Life

Modeling Life

The Mathematics of Biological Systems

  • Author: Alan Garfinkel,Jane Shevtsov,Yina Guo
  • Publisher: Springer
  • ISBN: 3319597310
  • Category: Mathematics
  • Page: 445
  • View: 8935
DOWNLOAD NOW »
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Quantization and Discretization at Large Scales

Quantization and Discretization at Large Scales

  • Author: edited by Florentin Smarandache, V. Christianto, Pavel Pintr
  • Publisher: Infinite Study
  • ISBN: 1599732270
  • Category:
  • Page: N.A
  • View: 7134
DOWNLOAD NOW »

The Butterfly in the Quantum World

The Butterfly in the Quantum World

The story of the most fascinating quantum fractal

  • Author: Indubala I Satija
  • Publisher: Morgan & Claypool Publishers
  • ISBN: 1681741172
  • Category: Science
  • Page: 350
  • View: 826
DOWNLOAD NOW »
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.

Nonlinearity, Chaos, and Complexity

Nonlinearity, Chaos, and Complexity

The Dynamics of Natural and Social Systems

  • Author: Cristoforo Sergio Bertuglia,Franco Vaio
  • Publisher: Oxford University Press on Demand
  • ISBN: 0198567901
  • Category: Mathematics
  • Page: 387
  • View: 9416
DOWNLOAD NOW »
Covering a broad range of topics and adopting a detailed philosophical approach to the subject, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences.

The Essence Of Chaos

The Essence Of Chaos

  • Author: Flavio Lorenzelli
  • Publisher: CRC Press
  • ISBN: 0203214587
  • Category: Science
  • Page: 227
  • View: 4254
DOWNLOAD NOW »
The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.