Chaotic Maps

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Chaotic Maps

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Author : Goong Chen
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Chaotic Maps written by Goong Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.

This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

Chaotic Maps

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Author : Goong Chen
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2011

Chaotic Maps written by Goong Chen and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

Chaotic Maps Fractals And Rapid Fluctuations

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Author : Liangliang Li
language : en
Publisher: Springer Nature
Release Date : 2025-07-15

Chaotic Maps Fractals And Rapid Fluctuations written by Liangliang Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Mathematics categories.

This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems.

Fully Chaotic Maps And Broken Time Symmetry

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Author : Dean J. Driebe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Fully Chaotic Maps And Broken Time Symmetry written by Dean J. Driebe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.

I am very pleased and privileged to write a short foreword for the monograph of Dean Driebe: Fully Chaotic Maps and Broken Time Symmetry. Despite the technical title this book deals with a problem of fundamental importance. To appreciate its meaning we have to go back to the tragic struggle that was initiated by the work of the great theoretical physicist Ludwig Boltzmann in the second half of the 19th century. Ludwig Boltzmann tried to emulate in physics what Charles Darwin had done in biology and to formulate an evolutionary approach in which past and future would play different roles. Boltzmann's work has lead to innumerable controversies as the laws of classical mechanics (as well as the laws of quan tum mechanics) as traditionally formulated imply symmetry between past and future. As is well known, Albert Einstein often stated that "Time is an illusion". Indeed, as long as dynamics is associated with trajectories satisfy ing the equations of classical mechanics, explaining irreversibility in terms of trajectories appears, as Henri Poincare concluded, as a logical error. After a long struggle, Boltzmann acknowledged his defeat and introduced a probabil ity description in which all microscopic states are supposed to have the same a priori probability. Irreversibility would then be due to the imperfection of our observations associated only with the "macroscopic" state described by temperature, pressure and other similar parameters. Irreversibility then appears devoid of any fundamental significance. However today this position has become untenable.

Multimedia Security Using Chaotic Maps Principles And Methodologies

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Author : Khalid M. Hosny
language : en
Publisher: Springer Nature
Release Date : 2020-02-28

Multimedia Security Using Chaotic Maps Principles And Methodologies written by Khalid M. Hosny and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Technology & Engineering categories.

This comprehensive book is primarily intended for researchers, engineers, mathematicians and computer security specialists who are interested in multimedia security, steganography, encryption, and related research fields. It is also a valuable reference resource for postgraduate and senior undergraduate students who are studying multimedia, multimedia security, and information security, as well as for professionals in the IT industry.

Advances In Data And Information Sciences

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Author : Mohan L. Kolhe
language : en
Publisher: Springer Nature
Release Date : 2020-01-02

Advances In Data And Information Sciences written by Mohan L. Kolhe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Technology & Engineering categories.

This book gathers a collection of high-quality peer-reviewed research papers presented at the 2nd International Conference on Data and Information Sciences (ICDIS 2019), held at Raja Balwant Singh Engineering Technical Campus, Agra, India, on March 29–30, 2019. In chapters written by leading researchers, developers, and practitioner from academia and industry, it covers virtually all aspects of computational sciences and information security, including central topics like artificial intelligence, cloud computing, and big data. Highlighting the latest developments and technical solutions, it will show readers from the computer industry how to capitalize on key advances in next-generation computer and communication technology.

Chaos Based Cryptography

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Author : Ljupco Kocarev
language : en
Publisher: Springer
Release Date : 2011-06-17

Chaos Based Cryptography written by Ljupco Kocarev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-17 with Technology & Engineering categories.

Chaos-based cryptography, attracting many researchers in the past decade, is a research field across two fields, i.e., chaos (nonlinear dynamic system) and cryptography (computer and data security). It Chaos' properties, such as randomness and ergodicity, have been proved to be suitable for designing the means for data protection. The book gives a thorough description of chaos-based cryptography, which consists of chaos basic theory, chaos properties suitable for cryptography, chaos-based cryptographic techniques, and various secure applications based on chaos. Additionally, it covers both the latest research results and some open issues or hot topics. The book creates a collection of high-quality chapters contributed by leading experts in the related fields. It embraces a wide variety of aspects of the related subject areas and provide a scientifically and scholarly sound treatment of state-of-the-art techniques to students, researchers, academics, personnel of law enforcement and IT practitioners who are interested or involved in the study, research, use, design and development of techniques related to chaos-based cryptography.

Progress In Mathematical Biology Research

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Author : James Terrence Kelly
language : en
Publisher: Nova Publishers
Release Date : 2008

Progress In Mathematical Biology Research written by James Terrence Kelly and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field. Some reasons for this include: the explosion of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools, recent development of mathematical tools such as chaos theory to help understand complex, non-linear mechanisms in biology, an increase in computing power which enables calculations and simulations to be performed that were not previously possible, and an increasing interest in in-silico experimentation due to the complications involved in human and animal research. This new book presents the latest leading-edge research in the field.

Soft Computing Theories And Applications

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Author : Rajesh Kumar
language : en
Publisher: Springer Nature
Release Date : 2023-04-24

Soft Computing Theories And Applications written by Rajesh Kumar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-24 with Technology & Engineering categories.

This book focuses on soft computing and how it can be applied to solve real-world problems arising in various domains, ranging from medicine and health care, to supply chain management, image processing and cryptanalysis. It gathers high-quality papers presented at the International Conference on Soft Computing: Theories and Applications (SoCTA 2022), held at University Institute of Technology, Himachal Pradesh University Shimla, Himachal Pradesh, India. The book offers valuable insights into soft computing for teachers and researchers alike; the book inspires further research in this dynamic field.

Intelligent Computing Based On Chaos

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Author : Ljupco Kocarev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-09

Intelligent Computing Based On Chaos written by Ljupco Kocarev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-09 with Mathematics categories.

Chaos is a fascinating phenomenon that has been observed in nature, laboratory, and has been applied in various real-world applications. Chaotic systems are deterministic with no random elements involved yet their behavior appears to be random. Obser- tions of chaotic behavior in nature include weather and climate, the dynamics of sat- lites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, to mention only a few examples. Chaos has been observed in the laboratory in a number of systems such as electrical circuits, lasers, chemical reactions, fluid dynamics, mechanical systems, and magneto-mechanical devices. Chaotic behavior has also found numerous applications in electrical and communication engineering, information and communication technologies, biology and medicine. To the best of our knowledge, this is the first book edited on chaos applications in intelligent computing. To access the latest research related to chaos applications in intelligent computing, we launched the book project where researchers from all over the world provide the necessary coverage of the mentioned field. The primary obj- tive of this project was to assemble as much research coverage as possible related to the field by defining the latest innovative technologies and providing the most c- prehensive list of research references.

Chaotic Maps

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