Handbook of Applications of Chaos Theory

Handbook of Applications of Chaos Theory
Title Handbook of Applications of Chaos Theory PDF eBook
Author Christos H. Skiadas
Publisher CRC Press
Pages 934
Release 2017-12-19
Genre Mathematics
ISBN 1466590440

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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.

Applied Chaos and Complexity Theory in Education

Applied Chaos and Complexity Theory in Education
Title Applied Chaos and Complexity Theory in Education PDF eBook
Author Erçetin, ?efika ?ule
Publisher IGI Global
Pages 322
Release 2016-05-23
Genre Education
ISBN 1522504613

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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 in the Social Sciences

Chaos Theory in the Social Sciences
Title Chaos Theory in the Social Sciences PDF eBook
Author L. Douglas Kiel
Publisher University of Michigan Press
Pages 358
Release 2009-11-10
Genre Political Science
ISBN 0472022520

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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.

Chaos Theory Tamed

Chaos Theory Tamed
Title Chaos Theory Tamed PDF eBook
Author Garnett Williams
Publisher CRC Press
Pages 518
Release 1997-09-09
Genre Mathematics
ISBN 1482295415

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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.

Chaos for Engineers

Chaos for Engineers
Title Chaos for Engineers PDF eBook
Author Tomasz Kapitaniak
Publisher Springer Science & Business Media
Pages 150
Release 2012-12-06
Genre Technology & Engineering
ISBN 3642571433

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

Chaos in Electronics

Chaos in Electronics
Title Chaos in Electronics PDF eBook
Author M.A. van Wyk
Publisher Springer Science & Business Media
Pages 489
Release 2013-06-29
Genre Technology & Engineering
ISBN 9401589216

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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.

Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities

Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities
Title Applied Nonlinear Dynamics And Chaos Of Mechanical Systems With Discontinuities PDF eBook
Author Bram De Kraker
Publisher World Scientific
Pages 462
Release 2000-04-28
Genre Technology & Engineering
ISBN 9814497908

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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.