Discrete Chaos

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Discrete Chaos, Second Edition

Saber N. Elaydi
Discrete Chaos Second Edition Book PDF

Author : Saber N. Elaydi
Publisher : CRC Press
Page : 441 pages
File Size : 52,9 Mb
Release : 2007-11-09
Category : Mathematics
ISBN : 9781584885924

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Discrete Chaos, Second Edition by Saber N. Elaydi Pdf

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CD-ROM and the MapleTM and Mathematica® code available for download online. Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.

Fractional Discrete Chaos: Theories, Methods And Applications

Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham
Fractional Discrete Chaos Theories Methods And Applications Book PDF

Author : Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham
Publisher : World Scientific
Page : 218 pages
File Size : 43,8 Mb
Release : 2023-02-13
Category : Science
ISBN : 9789811271229

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Fractional Discrete Chaos: Theories, Methods And Applications by Adel Ouannas,Iqbal M Batiha,Viet-thanh Pham Pdf

In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics.The aims of this book are as follows:

Chaos in Discrete Dynamical Systems

Ralph Abraham,Laura Gardini,Christian Mira
Chaos in Discrete Dynamical Systems Book PDF

Author : Ralph Abraham,Laura Gardini,Christian Mira
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 42,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461219361

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Chaos in Discrete Dynamical Systems by Ralph Abraham,Laura Gardini,Christian Mira Pdf

The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Introduction to Discrete Dynamical Systems and Chaos

Mario Martelli
Introduction to Discrete Dynamical Systems and Chaos Book PDF

Author : Mario Martelli
Publisher : John Wiley & Sons
Page : 347 pages
File Size : 42,8 Mb
Release : 2011-11-01
Category : Mathematics
ISBN : 9781118031124

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Introduction to Discrete Dynamical Systems and Chaos by Mario Martelli Pdf

A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

Discrete Dynamical Systems, Bifurcations and Chaos in Economics

Wei-Bin Zhang
Discrete Dynamical Systems Bifurcations and Chaos in Economics Book PDF

Author : Wei-Bin Zhang
Publisher : Elsevier
Page : 460 pages
File Size : 46,5 Mb
Release : 2006-01-05
Category : Mathematics
ISBN : 0080462464

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Discrete Dynamical Systems, Bifurcations and Chaos in Economics by Wei-Bin Zhang Pdf

This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics Mathematical definitions and theorems are introduced in a systematic and easily accessible way Examples are from almost all fields of economics; technically proceeding from basic to advanced topics Lively illustrations with numerous figures Numerous simulation to see paths of economic dynamics Comprehensive treatment of the subject with a comprehensive and easily accessible approach

Discrete Dynamical Systems and Chaotic Machines

Jacques Bahi,Christophe Guyeux
Discrete Dynamical Systems and Chaotic Machines Book PDF

Author : Jacques Bahi,Christophe Guyeux
Publisher : CRC Press
Page : 232 pages
File Size : 44,9 Mb
Release : 2013-06-07
Category : Computers
ISBN : 9781466554511

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Discrete Dynamical Systems and Chaotic Machines by Jacques Bahi,Christophe Guyeux Pdf

For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications shows how to make finite mac

Chaotic Dynamics of Fractional Discrete Time Systems

Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee
Chaotic Dynamics of Fractional Discrete Time Systems Book PDF

Author : Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee
Publisher : CRC Press
Page : 188 pages
File Size : 42,6 Mb
Release : 2024-09-06
Category : Mathematics
ISBN : 9781040051689

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Chaotic Dynamics of Fractional Discrete Time Systems by Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee Pdf

The book reviews the application of discrete fractional operators in diverse fields such as biological and chemical reactions, as well as chaotic systems, demonstrating their applications in physics. The dynamical analysis is carried out using equilibrium points of the system for studying their stability properties and the chaotic behaviors are illustrated with the help of bifurcation diagrams and Lyapunov exponents. The book is divided into three parts. Part I deals with the application of discrete fractional operators in chemical reaction-based systems with biological significance. Two different chemical reaction models are analysed- one being disproportionation of glucose, which plays an important role in human physiology and the other is the Lengyel – Epstein chemical model. Chaotic behavior of the systems is studied and the synchronization of the system is performed. Part II covers the analysis of biological systems like tumor immune system and neuronal models by introducing memristor based flux control. The memductance functions are considered as quadratic, periodic, and exponential functions. The final part of the book reviews the complex form of the Rabinovich-Fabrikant system which describes physical systems with strong nonlinearity exhibiting unusual behavior.

Discrete Chaos

Saber N. Elaydi
Discrete Chaos Book PDF

Author : Saber N. Elaydi
Publisher : CRC Press
Page : 440 pages
File Size : 45,6 Mb
Release : 2007-11-09
Category : Mathematics
ISBN : 9781420011043

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Discrete Chaos by Saber N. Elaydi Pdf

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determi

An Introduction to Difference Equations

Saber N. Elaydi
An Introduction to Difference Equations Book PDF

Author : Saber N. Elaydi
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 45,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475731101

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An Introduction to Difference Equations by Saber N. Elaydi Pdf

Integrating both classical and modern treatments of difference equations, this book contains the most updated and comprehensive material on stability, Z-transform, discrete control theory, asymptotic theory, continued fractions and orthogonal polynomials. While the presentation is simple enough for use by advanced undergraduates and beginning graduates in mathematics, engineering science, and economics, it will also be a useful reference for scientists and engineers interested in discrete mathematical models. The text covers a large set of applications in a variety of disciplines, including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, epidemic models and host-parasitoid systems, with each section rounded off by an extensive and highly selected set of exercises.

Advanced Research on Industry, Information System and Material Engineering, IISME2011

Helen Zhang,Gang Shen,David Jin
Advanced Research on Industry Information System and Material Engineering IISME2011 Book PDF

Author : Helen Zhang,Gang Shen,David Jin
Publisher : Trans Tech Publications Ltd
Page : 2400 pages
File Size : 43,6 Mb
Release : 2011-02-21
Category : Technology & Engineering
ISBN : 9783038135760

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Advanced Research on Industry, Information System and Material Engineering, IISME2011 by Helen Zhang,Gang Shen,David Jin Pdf

Volume is indexed by Thomson Reuters CPCI-S (WoS). In this special collection of over 470 peer-reviewed papers are to be found many original ideas and new angles on aspects of industry, information systems and materials engineering. It offers a good basis upon which researchers can exchange their innovative ideas from a new perspective. In addition, the proceedings provide guidance for scientists, physicists, chemists, teachers, etc. all over the world.

Chaos

Kathleen Alligood,Tim Sauer,J.A. Yorke
Chaos Book PDF

Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Page : 620 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642592812

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Chaos by Kathleen Alligood,Tim Sauer,J.A. Yorke Pdf

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.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Differential Equations Dynamical Systems and an Introduction to Chaos Book PDF

Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Page : 433 pages
File Size : 43,6 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780123497031

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Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch,Stephen Smale,Robert L. Devaney Pdf

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

An Introduction to Dynamical Systems and Chaos

G.C. Layek
An Introduction to Dynamical Systems and Chaos Book PDF

Author : G.C. Layek
Publisher : Springer
Page : 622 pages
File Size : 55,9 Mb
Release : 2015-12-01
Category : Mathematics
ISBN : 9788132225560

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An Introduction to Dynamical Systems and Chaos by G.C. Layek Pdf

The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

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

Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal
Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self excited Attractors Book PDF

Author : Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal
Publisher : MDPI
Page : 290 pages
File Size : 52,9 Mb
Release : 2019-05-03
Category : Technology & Engineering
ISBN : 9783038978985

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Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal Pdf

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.

Dynamics with Chaos and Fractals

Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Dynamics with Chaos and Fractals Book PDF

Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Publisher : Springer Nature
Page : 226 pages
File Size : 55,8 Mb
Release : 2020-01-01
Category : Mathematics
ISBN : 9783030358549

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Dynamics with Chaos and Fractals by Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily Pdf

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.