Discrete dynamical systems and chaotic machines: theory and applications PDF
Preview Discrete dynamical systems and chaotic machines: theory and applications
D Chapman & Hall/CRC Mathematics/Computer Science i s Numerical Analysis and Scientific Computing c r e For computer scientists, especially those in the security field, the use t e of chaos has been limited to the computation of a small collection D of famous but unsuitable maps that offer no explanation of why y chaos is relevant in the considered contexts. Discrete Dynamical n a Systems and Chaotic Machines: Theory and Applications shows Discrete m how to make finite machines, such as computers, neural networks, i c and wireless sensor networks, work chaotically as defined in a a rigorous mathematical framework. Taking into account that these l Dynamical Systems S machines must interact in the real world, the authors share their y s research results on the behaviors of discrete dynamical systems t and Chaotic Machines e and their use in computer science. m Covering both theoretical and practical aspects, the book presents: s a Theory and Applications • Key mathematical and physical ideas in chaos theory n • Computer science fundamentals, clearly establishing that d chaos properties can be satisfied by finite state machines C h • Concrete applications of chaotic machines in computer a security, including pseudorandom number generators, hash o t functions, digital watermarking, and steganography i c • Concrete applications of chaotic machines in wireless sensor M networks, including secure data aggregation and video a surveillance c h i Until the authors’ recent research, the practical implementation of n Jacques M. Bahi e the mathematical theory of chaos on finite machines raised several s issues. This self-contained book illustrates how chaos theory enables Christophe Guyeux the study of computer security problems, such as steganalysis, B a that otherwise could not be tackled. It also explains how the theory h i reinforces existing cryptographically secure tools and schemes. • G u y e u x K15321 K15321_Cover.indd 1 5/10/13 8:54 AM Discrete Dynamical Systems and Chaotic Machines Theory and Applications ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 1 5/13/13 12:06 PM CHAPMAN & HALL/CRC Numerical Analysis and Scientific Computing Aims and scope: Scientific computing and numerical analysis provide invaluable tools for the sciences and engineering. This series aims to capture new developments and summarize state-of-the-art methods over the whole spectrum of these fields. It will include a broad range of textbooks, monographs, and handbooks. Volumes in theory, including discretisation techniques, numerical algorithms, multiscale techniques, parallel and distributed algorithms, as well as applications of these methods in multi-disciplinary fields, are welcome. The inclusion of concrete real-world examples is highly encouraged. This series is meant to appeal to students and researchers in mathematics, engineering, and computational science. Editors Choi-Hong Lai Frédéric Magoulès School of Computing and Applied Mathematics and Mathematical Sciences Systems Laboratory University of Greenwich Ecole Centrale Paris Editorial Advisory Board Mark Ainsworth Peter Jimack Mathematics Department School of Computing Strathclyde University University of Leeds Todd Arbogast Takashi Kako Institute for Computational Department of Computer Science Engineering and Sciences The University of Electro-Communications The University of Texas at Austin Peter Monk Craig C. Douglas Department of Mathematical Sciences Computer Science Department University of Delaware University of Kentucky Francois-Xavier Roux Ivan Graham ONERA Department of Mathematical Sciences University of Bath Arthur E.P. Veldman Institute of Mathematics and Computing Science University of Groningen Proposals for the series should be submitted to one of the series editors above or directly to: CRC Press, Taylor & Francis Group 4th, Floor, Albert House 1-4 Singer Street London EC2A 4BQ UK ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 2 5/13/13 12:06 PM Published Titles Classical and Modern Numerical Analysis: Theory, Methods and Practice Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, and Padmanabhan Seshaiyer Cloud Computing: Data-Intensive Computing and Scheduling Frédéric Magoulès, Jie Pan, and Fei Teng Computational Fluid Dynamics Frédéric Magoulès A Concise Introduction to Image Processing using C++ Meiqing Wang and Choi-Hong Lai Decomposition Methods for Differential Equations: Theory and Applications Juergen Geiser Desktop Grid Computing Christophe Cérin and Gilles Fedak Discrete Dynamical Systems and Chaotic Machines: Theory and Applications Jacques M. Bahl and Christophe Guyeux Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations Daisuke Furihata and Takayasu Matsuo Grid Resource Management: Toward Virtual and Services Compliant Grid Computing Frédéric Magoulès, Thi-Mai-Huong Nguyen, and Lei Yu Fundamentals of Grid Computing: Theory, Algorithms and Technologies Frédéric Magoulès Handbook of Sinc Numerical Methods Frank Stenger Introduction to Grid Computing Frédéric Magoulès, Jie Pan, Kiat-An Tan, and Abhinit Kumar Iterative Splitting Methods for Differential Equations Juergen Geiser Mathematical Objects in C++: Computational Tools in a Unified Object-Oriented Approach Yair Shapira Numerical Linear Approximation in C Nabih N. Abdelmalek and William A. Malek Numerical Techniques for Direct and Large-Eddy Simulations Xi Jiang and Choi-Hong Lai Parallel Algorithms Henri Casanova, Arnaud Legrand, and Yves Robert Parallel Iterative Algorithms: From Sequential to Grid Computing Jacques M. Bahi, Sylvain Contassot-Vivier, and Raphael Couturier Particle Swarm Optimisation: Classical and Quantum Perspectives Jun Sun, Choi-Hong Lai, and Xiao-Jun Wu XML in Scientific Computing C. Pozrikidis ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 3 5/13/13 12:06 PM ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 4 5/13/13 12:06 PM Discrete Dynamical Systems and Chaotic Machines Theory and Applications Jacques M. Bahi Christophe Guyeux ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 5 5/13/13 12:06 PM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20130429 International Standard Book Number-13: 978-1-4665-5450-4 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copy- right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro- vides licenses and registration for a variety of users. For organizations that have been granted a pho- tocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com ©2013byTaylor&FrancisGroup,LLC K15321_FM.indd 6 5/13/13 12:06 PM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20130429 International Standard Book Number-13: 978-1-4665-5451-1 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copy- right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro- vides licenses and registration for a variety of users. For organizations that have been granted a pho- tocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com ©2013byTaylor&FrancisGroup,LLC CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2013 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20130429 International Standard Book Number-13: 978-1-4665-5450-4 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copy- right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro- vides licenses and registration for a variety of users. For organizations that have been granted a pho- tocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com ©2013byTaylor&FrancisGroup,LLC Contents List of Figures xi List of Tables xiii Preface xv Symbol Description xvii I An introduction to chaos 1 1 Classical Examples by Way of Introduction 3 1.1 Historical Context . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Feigenbaum’s Bifurcation . . . . . . . . . . . . . . . . . . . . 4 1.2.1 An iterative process . . . . . . . . . . . . . . . . . . . 4 1.2.2 Feigenbaum’s bifurcation . . . . . . . . . . . . . . . . 6 1.2.2.1 Presentation . . . . . . . . . . . . . . . . . . 6 1.2.2.2 Parameter µ between 0 and 0.75 . . . . . . . 6 1.2.2.3 Parameter µ between 0.75 and 1.25 . . . . . 6 1.2.2.4 Parameter between 1.25 and 1.368 . . . . . . 6 1.2.2.5 Summary . . . . . . . . . . . . . . . . . . . . 7 1.2.2.6 Parameter between 1.368 and 1.401 . . . . . 7 1.2.2.7 Parameter between 1.401 and 2 . . . . . . . 7 1.3 The Logistic Map . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Definition of the logistic map . . . . . . . . . . . . . . 8 1.3.2 Behavior of the sequence. . . . . . . . . . . . . . . . . 8 1.3.3 Sensitivity to the initial conditions . . . . . . . . . . . 8 1.4 The Lorenz System . . . . . . . . . . . . . . . . . . . . . . . 9 II The mathematical theory of chaos 13 2 Definitions and Notations 15 2.1 Topological and Metrical Spaces . . . . . . . . . . . . . . . . 15 2.1.1 Topological spaces, open sets, and neighborhoods . . . 15 2.1.1.1 First definitions . . . . . . . . . . . . . . . . 15 2.1.1.2 Examples of topologies . . . . . . . . . . . . 16 2.1.2 Distances, metrical spaces . . . . . . . . . . . . . . . . 16 2.2 Compactness and Completeness . . . . . . . . . . . . . . . . 17 v © 2013 by Taylor & Francis Group, LLC
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