Practical Numerical Algorithms for Chaotic Systems

Practical Numerical Algorithms for Chaotic Systems
Author: Thomas S. Parker
Publisher: Springer Science & Business Media
Total Pages: 354
Release: 2012-12-06
Genre: Science
ISBN: 1461234867
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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.

Construction of Arithmetical Meanings and Strategies

Construction of Arithmetical Meanings and Strategies
Author: Leslie Steffe
Publisher: Springer
Total Pages: 343
Release: 1987-12-18
Genre: Psychology
ISBN: 9780387966885
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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

Practical Bifurcation and Stability Analysis
Author: Rüdiger Seydel
Publisher: Springer Science & Business Media
Total Pages: 493
Release: 2009-12-14
Genre: Mathematics
ISBN: 144191739X
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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

Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization
Author: Esteban Tlelo-Cuautle
Publisher: CRC Press
Total Pages: 267
Release: 2021-05-09
Genre: Mathematics
ISBN: 100034665X
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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.

Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and Their Electronic Realization

Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and Their Electronic Realization
Author: Esteban Tlelo-Cuautle
Publisher: CRC Press
Total Pages: 0
Release: 2023-05
Genre:
ISBN: 9780367706333
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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.

Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications

Mem-elements for Neuromorphic Circuits with Artificial Intelligence Applications
Author: Christos Volos
Publisher: Academic Press
Total Pages: 570
Release: 2021-06-17
Genre: Technology & Engineering
ISBN: 0128232021
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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

Advances and Applications in Chaotic Systems
Author: Sundarapandian Vaidyanathan
Publisher: Springer
Total Pages: 600
Release: 2016-03-22
Genre: Technology & Engineering
ISBN: 3319302795
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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.

Chaos in Electric Drive Systems

Chaos in Electric Drive Systems
Author: K. T. Chau
Publisher: John Wiley & Sons
Total Pages: 336
Release: 2011-03-31
Genre: Science
ISBN: 0470828366
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In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives. The first book to comprehensively treat chaos in electric drive systems Reviews chaos in various electrical engineering technologies and drive systems Presents innovative approaches to stabilize and stimulate chaos in typical drives Discusses practical application of chaos stabilization, chaotic modulation and chaotic motion Authored by well-known scientists in the field Lecture materials available from the book's companion website This book is ideal for researchers and graduate students who specialize in electric drives, mechatronics, and electric machinery, as well as those enrolled in classes covering advanced topics in electric drives and control. Engineers and product designers in industrial electronics, consumer electronics, electric appliances and electric vehicles will also find this book helpful in applying these emerging techniques. Lecture materials for instructors available at www.wiley.com/go/chau_chaos

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications
Author: Esteban Tlelo-Cuautle
Publisher: Springer Nature
Total Pages: 212
Release: 2019-11-11
Genre: Technology & Engineering
ISBN: 303031250X
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This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.