A First Course In Chaotic Dynamical Systems

Theory And Experiment

Author: Robert L. Devaney

Publisher: Westview Press

ISBN: 9780813345475

Category: Science

Page: 320

View: 6869

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.

Exploring Chaos

Theory And Experiment

Author: Brian Davies

Publisher: CRC Press

ISBN: 0429971419

Category: Mathematics

Page: 256

View: 7760

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, Poincarections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software.

Time-Delayed Chaotic Dynamical Systems

From Theory to Electronic Experiment

Author: Tanmoy Banerjee,Debabrata Biswas

Publisher: Springer

ISBN: 3319709933

Category: Technology & Engineering

Page: 114

View: 8936

This book describes systematic design techniques for chaotic and hyperchaotic systems, the transition from one to the other, and their implementation in electronic circuits. It also discusses the collective phenomena manifested by these systems when connected by a physical coupling scheme. Readers will be introduced to collective behaviours, such as synchronization and oscillation suppression, and will learn how to implement nonlinear differential equations in electronic circuits. Further, the book shows how the choice of nonlinearity can lead to chaos and hyperchaos, even in a first-order time-delayed system. The occurrence of these phenomena, together with the efficiency of the design techniques described, is presented with theoretical studies, numerical characterization and experimental demonstrations with the corresponding electronic circuits, helping readers grasp the design aspects of dynamical systems as a whole in electronic circuits. The authors then discuss the usefulness of an active all-pass filter as the delay element, supported by their own experimental observations, as well as theoretical and numerical results. Including detailed analysis, as well as computations with suitable dedicated software packages, the book will be of interest to all academics and researchers who wish to expand their knowledge of the subtlety of nonlinear time-delayed systems. It also offers a valuable source of information for engineers, linking the design techniques of chaotic time-delayed systems with their collective phenomena.

An Experimental Approach to Nonlinear Dynamics and Chaos

Author: Nicholas Tufillaro,Tyler Abbott

Publisher: Addison Wesley Publishing Company


Category: Chaotic behavior in systems.

Page: 420

View: 7417

This essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories.

Applications of Chaos and Nonlinear Dynamics in Science and Engineering -

Author: Santo Banerjee,Lamberto Rondoni

Publisher: Springer

ISBN: 3642340172

Category: Science

Page: 296

View: 7513

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.


The Geometry Of Behavior

Author: Ralph H. Abraham,Christopher D. Shaw

Publisher: Addison-Wesley Longman


Category: Dynamics

Page: 642

View: 4154


Encyclopedia of Social Work

1997 Supplement

Author: Richard L. Edwards

Publisher: N A S W Press

ISBN: 9780871012777

Category: Encyclopedias and dictionaries

Page: 428

View: 3206


Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Volume 20 : Biomedical Engineering Towards the Year 2000 and Beyond : Hong Kong SAR, China, October 29-November 1, 1998

Author: IEEE Engineering in Medicine and Biology Society. Conference

Publisher: N.A

ISBN: 9780780351646

Category: Biomedical engineering

Page: 3384

View: 1970

These proceedings document the 20th Annual International Conference of the IEEE/EMB Society held in Amsterdam in 1998. Covering the entire field of biomedical including the latest development in instrumentation, neourotechnology, rehabilitation engineering, imaging signal & image processing, cardiac system, neuromuscular system, sensory systems, physiological system modeling, measurement techniques, clinical engineering & tissue engineering. Partial Contents: Cardiovascular Systems; Medical Imaging; Clinical Engineering; Medical Informatics; Signal Processing; Neuromuscular Systems; Biomechanics; Physiological Systems; Modeling & Identification; Instrumentation

Who Gave You the Epsilon?

And Other Tales of Mathematical History

Author: Marlow Anderson,Victor Katz,Robin Wilson

Publisher: MAA

ISBN: 9780883855690

Category: Mathematics

Page: 431

View: 4771

Follows on from Sherlock Holmes in Babylon to take the history of mathematics through the nineteenth and twentieth centuries.


Author: N.A

Publisher: N.A


Category: Electrical engineering

Page: N.A

View: 2565


IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics

Proceedings of the IUTAM Symposium held in Rome, Italy, 8-13 June 2003

Author: Giuseppe Rega,F. Vestroni

Publisher: Springer Science & Business Media

ISBN: 9781402032677

Category: Technology & Engineering

Page: 510

View: 5311

The interest of the applied mechanics community in chaotic dynamics of engineering systems has exploded in the last fifteen years, although research activity on nonlinear dynamical problems in mechanics started well before the end of the Eighties. It developed first within the general context of the classical theory of nonlinear oscillations, or nonlinear vibrations, and of the relevant engineering applications. This was an extremely fertile field in terms of formulation of mechanical and mathematical models, of development of powerful analytical techniques, and of understanding of a number of basic nonlinear phenomena. At about the same time, meaningful theoretical results highlighting new solution methods and new or complex phenomena in the dynamics of deterministic systems were obtained within dynamical systems theory by means of sophisticated geometrical and computational techniques. In recent years, careful experimental studies have been made to establish the actual occurrence and observability of the predicted dynamic phenomena, as it is vitally needed in all engineering fields. Complex dynamics have been shown to characterize the behaviour of a great number of nonlinear mechanical systems, ranging from aerospace engineering applications to naval applications, mechanical engineering, structural engineering, robotics and biomechanics, and other areas. The International Union of Theoretical and Applied Mechanics grasped the importance of such complex phenomena in the Eighties, when the first IUTAM Symposium devoted to the general topic of nonlinear and chaotic dynamics in applied mechanics and engineering was held in Stuttgart (1989).

Cellular Automata

Theory and Experiment

Author: Howard Gutowitz

Publisher: MIT Press

ISBN: 9780262570862

Category: Science

Page: 483

View: 6168

The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software.

Zufall und Chaos

Author: David Ruelle

Publisher: Springer

ISBN: 9783540577867

Category: Science

Page: 254

View: 1953

"Das Buch des Mathematikers und Physikers David Ruelle ist amüsant und lehrreich. Amüsant, weil es aus der seltsamen Welt der Mathematiker berichtet, und lehrreich, weil es die Grundideen schwieriger Theorien einfach darstellt... Ich habe das erfreulich kurze Buch mit großem Vergnügen gelesen und empfehle es jedem, der Spaß an spielerisch vorgetragenen genauen Überlegungen hat..." #Prof. Dr. Henning Genz, Spektrum der Wissenschaft 7/93#

Chaotic Behaviour of Deterministic Dissipative Systems

Author: Milos Marek,Igor Schreiber

Publisher: Cambridge University Press

ISBN: 9780521438308

Category: Science

Page: 367

View: 2153

Surveying both theoretical and experimental aspects of chaotic behavior, this book presents chaos as a model for many seemingly random processes in nature. Basic notions from the theory of dynamical systems, bifurcation theory and the properties of chaotic solutions are then described and illustrated by examples. A review of numerical methods used both in studies of mathematical models and in the interpretation of experimental data is also provided. In addition, an extensive survey of experimental observation of chaotic behavior and methods of its analysis are used to stress universal features of the phenomenon.

Nonlinear Acoustics

Author: K.A. Naugol'nikh,L.A. Ostrovsky

Publisher: Springer Science & Business Media

ISBN: 9781563963384

Category: Science

Page: 313

View: 865

Market: Acousticians, research scientists, instructors, and graduate and advanced undergraduate students in nonlinear acoustics. This book contains a collection of papers by authors of the Former Soviet Union. The topics covered are media with "structural" nonlinearities, optical generation of sound, acoustic beat-wave interactions, acoustic shock waves, thermal self-focusing of acoustic waves, solitons, statistical nonlinear acoustics, media with relaxation and oscillatory degrees of freedom, parametric arrays, and fluid cavitation.