Chaotic Maps

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Chaotic Maps

Author : Goong Chen
Publisher : Springer Nature
ISBN 13 : 3031024036
Total Pages : 227 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Chaotic Maps by : Goong Chen

Download or read book Chaotic Maps written by Goong Chen and published by Springer Nature. This book was released on 2022-05-31 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Multimedia Security Using Chaotic Maps: Principles and Methodologies

Author : Khalid M. Hosny
Publisher : Springer Nature
ISBN 13 : 3030387003
Total Pages : 271 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Multimedia Security Using Chaotic Maps: Principles and Methodologies by : Khalid M. Hosny

Download or read book Multimedia Security Using Chaotic Maps: Principles and Methodologies written by Khalid M. Hosny and published by Springer Nature. This book was released on 2020-02-28 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fully Chaotic Maps and Broken Time Symmetry

Author : Dean J. Driebe
Publisher : Springer Science & Business Media
ISBN 13 : 9780792355649
Total Pages : 180 pages
Book Rating : 4.3/5 (556 download)

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Book Synopsis Fully Chaotic Maps and Broken Time Symmetry by : Dean J. Driebe

Download or read book Fully Chaotic Maps and Broken Time Symmetry written by Dean J. Driebe and published by Springer Science & Business Media. This book was released on 1999-02-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book providing an introduction to a new approach to the nonequilibrium statistical mechanics of chaotic systems. It shows how the dynamical problem in fully chaotic maps may be solved on the level of evolving probability densities. On this level, time evolution is governed by the Frobenius-Perron operator. Spectral decompositions of this operator for a variety of systems are constructed in generalized function spaces. These generalized spectral decompositions are of special interest for systems with invertible trajectory dynamics, as on the statistical level the new solutions break time symmetry and allow for a rigorous understanding of irreversibility. Several techniques for the construction of explicit spectral decompositions are given. Systems ranging from the simple one-dimensional Bernoulli map to an invertible model of deterministic diffusion are treated in detail. Audience: Postgraduate students and researchers in chaos, dynamical systems and statistical mechanics.

Fully Chaotic Maps and Broken Time Symmetry

Author : Dean J. Driebe
Publisher : Springer Science & Business Media
ISBN 13 : 9401716285
Total Pages : 173 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Fully Chaotic Maps and Broken Time Symmetry by : Dean J. Driebe

Download or read book Fully Chaotic Maps and Broken Time Symmetry written by Dean J. Driebe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Logistic Map and the Route to Chaos

Author : Marcel Ausloos
Publisher : Springer Science & Business Media
ISBN 13 : 3540320237
Total Pages : 413 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Logistic Map and the Route to Chaos by : Marcel Ausloos

Download or read book The Logistic Map and the Route to Chaos written by Marcel Ausloos and published by Springer Science & Business Media. This book was released on 2006-02-11 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Chaos

Author : Kathleen Alligood
Publisher : Springer
ISBN 13 : 3642592813
Total Pages : 620 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Chaos by : Kathleen Alligood

Download or read book Chaos written by Kathleen Alligood and published by Springer. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Handbook of Research on Modeling, Analysis, and Control of Complex Systems

Author : Azar, Ahmad Taher
Publisher : IGI Global
ISBN 13 : 1799857905
Total Pages : 685 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Handbook of Research on Modeling, Analysis, and Control of Complex Systems by : Azar, Ahmad Taher

Download or read book Handbook of Research on Modeling, Analysis, and Control of Complex Systems written by Azar, Ahmad Taher and published by IGI Global. This book was released on 2020-12-05 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current literature on dynamic systems is quite comprehensive, and system theory’s mathematical jargon can remain quite complicated. Thus, there is a need for a compendium of accessible research that involves the broad range of fields that dynamic systems can cover, including engineering, life sciences, and the environment, and which can connect researchers in these fields. The Handbook of Research on Modeling, Analysis, and Control of Complex Systems is a comprehensive reference book that describes the recent developments in a wide range of areas including the modeling, analysis, and control of dynamic systems, as well as explores related applications. The book acts as a forum for researchers seeking to understand the latest theory findings and software problem experiments. Covering topics that include chaotic maps, predictive modeling, random bit generation, and software bug prediction, this book is ideal for professionals, academicians, researchers, and students in the fields of electrical engineering, computer science, control engineering, robotics, power systems, and biomedical engineering.

Advances in Data and Information Sciences

Author : Mohan L. Kolhe
Publisher : Springer Nature
ISBN 13 : 9811506949
Total Pages : 679 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Advances in Data and Information Sciences by : Mohan L. Kolhe

Download or read book Advances in Data and Information Sciences written by Mohan L. Kolhe and published by Springer Nature. This book was released on 2020-01-02 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Intelligent Computing Based on Chaos

Author : Ljupco Kocarev
Publisher : Springer Science & Business Media
ISBN 13 : 3540959718
Total Pages : 381 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Intelligent Computing Based on Chaos by : Ljupco Kocarev

Download or read book Intelligent Computing Based on Chaos written by Ljupco Kocarev and published by Springer Science & Business Media. This book was released on 2009-06-09 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics on Chaotic Systems

Author : Christos H. Skiadas
Publisher : World Scientific
ISBN 13 : 9814271349
Total Pages : 435 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Topics on Chaotic Systems by : Christos H. Skiadas

Download or read book Topics on Chaotic Systems written by Christos H. Skiadas and published by World Scientific. This book was released on 2009 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.

Chaos-based Cryptography

Author : Ljupco Kocarev
Publisher : Springer Science & Business Media
ISBN 13 : 3642205410
Total Pages : 400 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Chaos-based Cryptography by : Ljupco Kocarev

Download or read book Chaos-based Cryptography written by Ljupco Kocarev and published by Springer Science & Business Media. This book was released on 2011-06-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

13th Chaotic Modeling and Simulation International Conference

Author : Christos H. Skiadas
Publisher : Springer Nature
ISBN 13 : 3030707954
Total Pages : 1080 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis 13th Chaotic Modeling and Simulation International Conference by : Christos H. Skiadas

Download or read book 13th Chaotic Modeling and Simulation International Conference written by Christos H. Skiadas and published by Springer Nature. This book was released on 2021-12-14 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.

Chaotic Dynamics of Nonlinear Systems

Author : S. Neil Rasband
Publisher : Courier Dover Publications
ISBN 13 : 0486795993
Total Pages : 244 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Chaotic Dynamics of Nonlinear Systems by : S. Neil Rasband

Download or read book Chaotic Dynamics of Nonlinear Systems written by S. Neil Rasband and published by Courier Dover Publications. This book was released on 2015-08-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the concepts, applications, theory, and technique of chaos. Suitable for advanced undergraduates and graduate students and researchers. Requires familiarity with differential equations and linear vector spaces. 1990 edition.

Handbook of Chaos Control

Author : Eckehard Schöll
Publisher : John Wiley & Sons
ISBN 13 : 3527622322
Total Pages : 849 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Handbook of Chaos Control by : Eckehard Schöll

Download or read book Handbook of Chaos Control written by Eckehard Schöll and published by John Wiley & Sons. This book was released on 2008-09-08 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community. An interdisciplinary approach of interest to scientists and engineers working in a number of areas.

Chaos Analysis and Chaotic EMI Suppression of DC-DC Converters

Author : Bo Zhang
Publisher : John Wiley & Sons
ISBN 13 : 1118451112
Total Pages : 258 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Chaos Analysis and Chaotic EMI Suppression of DC-DC Converters by : Bo Zhang

Download or read book Chaos Analysis and Chaotic EMI Suppression of DC-DC Converters written by Bo Zhang and published by John Wiley & Sons. This book was released on 2014-11-11 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC converters due to wide applications of various electronic devices in industry and daily life, and the question of how to reduce the annoying, harmful EMI has attracted much research interest. This book focuses on the analysis and application of chaos to reduce harmful EMI of DC-DC converters. After a review of the fundamentals of chaos behaviors of DC-DC converters, the authors present some recent findings such as Symbolic Entropy, Complexity and Chaos Point Process, to analyze the characters of chaotic DC-DC converters. Using these methods, the statistic characters of chaotic DC-DC converters are extracted and the foundations for the following researches of chaotic EMI suppression are reinforced. The focus then transfers to estimating the power spectral density of chaotic PWM converters behind an introduction of basic principles of spectrum analysis and chaotic PWM technique. Invariant Density, and Prony and Wavelet analysis methods are suggested for estimating the power spectral density of chaotic PWM converters. Finally, some design-oriented applications provide a good example of applying chaos theory in engineering practice, and illustrate the effectiveness on suppressing EMI of the proposed chaotic PWM. Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design Approaches the subject in a systematic manner from analyzing method, chaotic phenomenon and EMI characteristics, analytical methods for chaos, and applying chaos to reduce EMI (electromagnetic interference) Highlights advanced research work in the fields of statistic characters of nonlinear behaviors and chaotic PWM technology to suppress EMI of switching converters Bridges the gap between numerical theory and real-world applications, enabling power electronics designers to both analyze the effects of chaos and leverage these effects to reduce EMI

Nonlinear Maps and their Applications

Author : Ricardo López-Ruiz
Publisher : Springer
ISBN 13 : 3319123289
Total Pages : 291 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Nonlinear Maps and their Applications by : Ricardo López-Ruiz

Download or read book Nonlinear Maps and their Applications written by Ricardo López-Ruiz and published by Springer. This book was released on 2015-03-11 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics, biology, or can also be obtained via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists. This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2013) held in Zaragoza, Spain, on September 3-4, 2013. This kind of collaborative effort is of paramount importance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well as researchers in the field.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Author : Christos Volos
Publisher : MDPI
ISBN 13 : 3038978981
Total Pages : 290 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by : Christos Volos

Download or read book Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors written by Christos Volos and published by MDPI. This book was released on 2019-05-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.