Practical Numerical Algorithms For Chaotic Systems
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Practical Numerical Algorithms For Chaotic Systems
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Author : Thomas S. Parker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Practical Numerical Algorithms For Chaotic Systems written by Thomas S. Parker 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 2012-12-06 with Science categories.
One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.
Practical Numerical Algorithms For Chaotic Systems
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Author : Thomas S Parker
language : en
Publisher:
Release Date : 1989-08-01
Practical Numerical Algorithms For Chaotic Systems written by Thomas S Parker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-01 with categories.
Construction Of Arithmetical Meanings And Strategies
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Author : Leslie Steffe
language : en
Publisher: Springer
Release Date : 1987-12-18
Construction Of Arithmetical Meanings And Strategies written by Leslie Steffe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-18 with Psychology categories.
The studies presented in this book should be of interest to anybody concerned with the teaching of arithmetic to young children or with cognitive development in general. The 'eaching experiment· was carried out with half a dozen children entering first grade over two years in biweekly sessions. Methodologically the authors' research is original. It is a longitudinal but not a naturalistic study, since the experimenter-teachers directed their interaction with each individual child with a view to his or her possible progress. It is experimental in the sense that two groups of subjects were selected according to criteria derived from an earlier study (Steffe, von Glasersfeld, Richards & Cobb, 1983) and that the problems proposed were comparable, though far from identical across the subjects; but unlike more rigid and shorter "learning" or ''training" studies it does not include pre-and posttests, or predetermined procedures. Theoretically, the authors subscribe to Piagefs constructivism: numbers are made by children, not found (as they may find some pretty rocks, for example) or accepted from adults (as they may accept and use a toy). The authors interpret changes in the children's counting behaviors in terms of constructivist concepts such as assimilation, accommodation, and reflective abstraction, and certain excerpts from protocols provide on-line examples of such processes at work. They also subscribe to Vygotsky's proposal for teachers '0 utilize the zone of proximal development and to lead the child to what he (can) not yet do· (1965, p. 104).
Practical Bifurcation And Stability Analysis
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Author : Rüdiger Seydel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-14
Practical Bifurcation And Stability Analysis written by Rüdiger Seydel 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 2009-12-14 with Mathematics categories.
Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.
Optimization Of Integer Fractional Order Chaotic Systems By Metaheuristics And Their Electronic Realization
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Author : Esteban Tlelo-Cuautle
language : en
Publisher: CRC Press
Release Date : 2021
Optimization Of Integer Fractional Order Chaotic Systems By Metaheuristics And Their Electronic Realization written by Esteban Tlelo-Cuautle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Chaotic behavior in systems categories.
"CRC Press is an imprint of the Taylor & Francis Group, an Informa business."
Optimization Of Integer Fractional Order Chaotic Systems By Metaheuristics And Their Electronic Realization
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Author : Esteban Tlelo-Cuautle
language : en
Publisher: CRC Press
Release Date : 2021-05-09
Optimization Of Integer Fractional Order Chaotic Systems By Metaheuristics And Their Electronic Realization written by Esteban Tlelo-Cuautle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-09 with Mathematics categories.
Mathematicians have devised different chaotic systems that are modeled by integer or fractional-order differential equations, and whose mathematical models can generate chaos or hyperchaos. The numerical methods to simulate those integer and fractional-order chaotic systems are quite different and their exactness is responsible in the evaluation of characteristics like Lyapunov exponents, Kaplan-Yorke dimension, and entropy. One challenge is estimating the step-size to run a numerical method. It can be done analyzing the eigenvalues of self-excited attractors, while for hidden attractors it is difficult to evaluate the equilibrium points that are required to formulate the Jacobian matrices. Time simulation of fractional-order chaotic oscillators also requires estimating a memory length to achieve exact results, and it is associated to memories in hardware design. In this manner, simulating chaotic/hyperchaotic oscillators of integer/fractional-order and with self-excited/hidden attractors is quite important to evaluate their Lyapunov exponents, Kaplan-Yorke dimension and entropy. Further, to improve the dynamics of the oscillators, their main characteristics can be optimized applying metaheuristics, which basically consists of varying the values of the coefficients of a mathematical model. The optimized models can then be implemented using commercially available amplifiers, field-programmable analog arrays (FPAA), field-programmable gate arrays (FPGA), microcontrollers, graphic processing units, and even using nanometer technology of integrated circuits. The book describes the application of different numerical methods to simulate integer/fractional-order chaotic systems. These methods are used within optimization loops to maximize positive Lyapunov exponents, Kaplan-Yorke dimension, and entropy. Single and multi-objective optimization approaches applying metaheuristics are described, as well as their tuning techniques to generate feasible solutions that are suitable for electronic implementation. The book details several applications of chaotic oscillators such as in random bit/number generators, cryptography, secure communications, robotics, and Internet of Things.
New Methods For Chaotic Dynamics
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Author : Nikolai Aleksandrovich Magnitskii
language : en
Publisher: World Scientific
Release Date : 2006
New Methods For Chaotic Dynamics written by Nikolai Aleksandrovich Magnitskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations including nonlinear partial differential equations and differential equations with delay arguments. The transition is described from the Feigenbaum cascade of period doubling bifurcations of the original singular cycle to the complete or incomplete Sharkovskii subharmonic cascade of bifurcations of stable limit cycles with arbitrary period and finally to the complete or incomplete homoclinic cascade of bifurcations. The book presents a distinct view point on the principles of formation, scenarios of occurrence and ways of control of chaotic motion in nonlinear dissipative dynamical systems. All theoretical results and conclusions of the theory are strictly proved and confirmed by numerous examples, illustrations and numerical calculations. Sample Chapter(s). Chapter 1: Systems of Ordinary Differential Equations (1,736 KB). Contents: Systems of Ordinary Differential Equations; Bifurcations in Nonlinear Systems of Ordinary Differential Equations; Chaotic Systems of Ordinary Differential Equations; Principles of the Theory of Dynamical Chaos in Dissipative Systems of Ordinary Differential Equations; Dynamical Chaos in Infinitely-Dimensional Systems of Differential Equations; Chaos Control in Systems of Differential Equations. Readership: Graduate students and researchers in complex and chaotic dynamical systems.
The Art Of Modeling Dynamic Systems
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Author : Foster Morrison
language : en
Publisher: Courier Corporation
Release Date : 2012-03-07
The Art Of Modeling Dynamic Systems written by Foster Morrison and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-07 with Mathematics categories.
This text illustrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. It describes the benefits and limitations of the available modeling tools, showing engineers and scientists how any system can be rendered simpler and more predictable. Written by a well-known authority in the field, this volume employs practical examples and analogies to make models more meaningful. The more universal methods appear in considerable detail, and advanced dynamic principles feature easy-to-understand examples. The text draws careful distinctions between mathematical abstractions and observable realities. Additional topics include the role of pure mathematics, the limitations of numerical methods, forecasting in the presence of chaos and randomness, and dynamics without calculus. Specialized techniques and case histories are coordinated with a carefully selected and annotated bibliography. The original edition was a Library of Science Main Selection in May, 1991. This new Dover edition features corrections by the author and a new Preface.
Mem Elements For Neuromorphic Circuits With Artificial Intelligence Applications
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Author : Christos Volos
language : en
Publisher: Academic Press
Release Date : 2021-06-17
Mem Elements For Neuromorphic Circuits With Artificial Intelligence Applications written by Christos Volos and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-17 with Technology & Engineering categories.
Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications illustrates recent advances in the field of mem-elements (memristor, memcapacitor, meminductor) and their applications in nonlinear dynamical systems, computer science, analog and digital systems, and in neuromorphic circuits and artificial intelligence. The book is mainly devoted to recent results, critical aspects and perspectives of ongoing research on relevant topics, all involving networks of mem-elements devices in diverse applications. Sections contribute to the discussion of memristive materials and transport mechanisms, presenting various types of physical structures that can be fabricated to realize mem-elements in integrated circuits and device modeling. As the last decade has seen an increasing interest in recent advances in mem-elements and their applications in neuromorphic circuits and artificial intelligence, this book will attract researchers in various fields. Covers a broad range of interdisciplinary topics between mathematics, circuits, realizations, and practical applications related to nonlinear dynamical systems, nanotechnology, analog and digital systems, computer science and artificial intelligence Presents recent advances in the field of mem-elements (memristor, memcapacitor, meminductor) Includes interesting applications of mem-elements in nonlinear dynamical systems, analog and digital systems, neuromorphic circuits, computer science and artificial intelligence
Advances And Applications In Chaotic Systems
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Author : Sundarapandian Vaidyanathan
language : en
Publisher: Springer
Release Date : 2016-03-22
Advances And Applications In Chaotic Systems written by Sundarapandian Vaidyanathan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Technology & Engineering categories.
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.