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Handbook of Applications of Chaos Theory

Author : Christos H. Skiadas

Publisher : CRC Press

Page : 934 pages

File Size : 43,62 MB

Release : 2017-12-19

Category : Mathematics

ISBN : 1466590440

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Book Description

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.



Chaos Theory in the Social Sciences

Author : L. Douglas Kiel

Publisher : University of Michigan Press

Page : 358 pages

File Size : 47,18 MB

Release : 2009-11-10

Category : Political Science

ISBN : 0472022520

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Book Description

Chaos Theory in the Social Sciences: Foundations and Applications offers the most recent thinking in applying the chaos paradigm to the social sciences. The book explores the methodological techniques--and their difficulties--for determining whether chaotic processes may in fact exist in a particular instance and examines implications of chaos theory when applied specifically to political science, economics, and sociology. The contributors to the book show that no single technique can be used to diagnose and describe all chaotic processes and identify the strengths and limitations of a variety of approaches. The essays in this volume consider the application of chaos theory to such diverse phenomena as public opinion, the behavior of states in the international arena, the development of rational economic expectations, and long waves. Contributors include Brian J. L. Berry, Thad Brown, Kenyon B. DeGreene, Dimitrios Dendrinos, Euel Elliott, David Harvey, L. Ted Jaditz, Douglas Kiel, Heja Kim, Michael McBurnett, Michael Reed, Diana Richards, J. Barkley Rosser, Jr., and Alvin M. Saperstein. L. Douglas Kiel and Euel W. Elliott are both Associate Professors of Government, Politics, and Political Economy, University of Texas at Dallas.



Applied Chaos and Complexity Theory in Education

Author : Erçetin, ?efika ?ule

Publisher : IGI Global

Page : 322 pages

File Size : 14,8 MB

Release : 2016-05-23

Category : Education

ISBN : 1522504613

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Book Description

As a field of mathematical study, chaos and complexity theory analyzes the state of dynamical systems by evaluating how they interact, evolve, and adapt. Though this theory impacts a variety of disciplines, it also has significant influence on educational systems and settings. Applied Chaos and Complexity Theory in Education examines the application of the theories of chaos and complexity in relation to educational systems and institutions. Featuring emergent research and perspectives on mathematical patterns in educational settings and instructional practices, this book is a comprehensive reference source for researchers, scholars, mathematicians, and graduate students.



Chaos Theory Tamed

Author : Garnett Williams

Publisher : CRC Press

Page : 518 pages

File Size : 45,70 MB

Release : 1997-09-09

Category : Mathematics

ISBN : 1482295415

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Book Description

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.



Models and Applications of Chaos Theory in Modern Sciences

Author : Elhadj Zeraoulia

Publisher : CRC Press

Page : 738 pages

File Size : 43,66 MB

Release : 2011-09-07

Category : Mathematics

ISBN : 1439883408

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Book Description

This book presents a select group of papers that provide a comprehensive view of the models and applications of chaos theory in medicine, biology, ecology, economy, electronics, mechanical, and the human sciences. Covering both the experimental and theoretical aspects of the subject, it examines a range of current topics of interest. It consid



Chaos in Electronics

Author : M.A. van Wyk

Publisher : Springer Science & Business Media

Page : 489 pages

File Size : 35,78 MB

Release : 2013-06-29

Category : Technology & Engineering

ISBN : 9401589216

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Book Description

Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.



Chaos for Engineers

Author : Tomasz Kapitaniak

Publisher : Springer Science & Business Media

Page : 150 pages

File Size : 28,33 MB

Release : 2012-12-06

Category : Technology & Engineering

ISBN : 3642571433

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Book Description

A desription of the new mathematical ideas in nonlinear dynamics in such a way that engineers can apply them to real physical systems.



Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities

Author : Bram De Kraker

Publisher : World Scientific

Page : 462 pages

File Size : 46,21 MB

Release : 2000-04-28

Category : Technology & Engineering

ISBN : 9814497908

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Book Description

Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes.The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos.The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting.



Applications of Chaos and Nonlinear Dynamics in Engineering -

Author : Santo Banerjee

Publisher : Springer Science & Business Media

Page : 349 pages

File Size : 20,74 MB

Release : 2011-09-10

Category : Technology & Engineering

ISBN : 3642219217

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Book Description

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 volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). 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



Fractal Market Analysis

Author : Edgar E. Peters

Publisher : John Wiley & Sons

Page : 352 pages

File Size : 28,93 MB

Release : 1994-02-08

Category : Business & Economics

ISBN : 9780471585244

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Book Description

A leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena.