Practical Numerical Algorithms for Chaotic Systems
Practical Numerical Algorithms for Chaotic Systems

Author: Thomas S. Parker

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 354

ISBN-13: 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.

Practical Bifurcation and Stability Analysis
Practical Bifurcation and Stability Analysis

Author: Rüdiger Seydel

Publisher: Springer Science & Business Media

Published: 2009-12-14

Total Pages: 493

ISBN-13: 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.

Construction of Arithmetical Meanings and Strategies
Construction of Arithmetical Meanings and Strategies

Author: Leslie Steffe

Publisher: Springer

Published: 1987-12-18

Total Pages: 343

ISBN-13: 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).

Intelligent Computing Based on Chaos
Intelligent Computing Based on Chaos

Author: Ljupco Kocarev

Publisher: Springer Science & Business Media

Published: 2009-06-09

Total Pages: 381

ISBN-13: 3540959718

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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.

Semi-analytic Methods for the Navier-Stokes Equations
Semi-analytic Methods for the Navier-Stokes Equations

Author: Katie Coughlin

Publisher: American Mathematical Soc.

Published: 1999-04-18

Total Pages: 144

ISBN-13: 9780821895177

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The lectures collected for this volume were given during a workshop entitled, ``Semi-analytic Methods for the Navier Stokes Equations'' held at the CRM in Montreal. The title reflects the current reality in fluid dynamics: Navier-Stokes equations (NSE) describe the behavior of fluid in a wide range of physical situations, the solutions of these equations are sufficiently complicated, so that another level of analysis is clearly needed. The fundamental problem is not just to solve the NSE, but also to understand what the solutions mean. One of the goals of the workshop was to bring together people who, while working in different fields, share a common perspective on the nature of the problem to be solved. The lectures present a diverse set of techniques for modelling, computing, and understanding phenomena such as instabilities, turbulence and spatiotemporal chaos in fluids.

Hybrid Systems: Computation and Control
Hybrid Systems: Computation and Control

Author: Alberto Bemporad

Publisher: Springer

Published: 2007-05-31

Total Pages: 812

ISBN-13: 3540714936

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This book constitutes the refereed proceedings of the 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007, held in Pisa, Italy in April 2007. Among the topics addressed are models of heterogeneous systems, computability and complexity issues, real-time computing and control, embedded and resource-aware control, control and estimation over wireless networks, and programming languages support and implementation.

Chaos Control
Chaos Control

Author: Guanrong Chen

Publisher: Springer Science & Business Media

Published: 2003-07-25

Total Pages: 392

ISBN-13: 9783540404057

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Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. There exists no similar control theory-oriented book available in the market that is devoted to the subject of chaos control, written by control engineers for control engineers. World-renowned leading experts in the field provide their state-of-the-art survey about the extensive research that has been done over the last few years in this subject. The new technology of chaos control has major impact on novel engineering applications such as telecommunications, power systems, liquid mixing, internet technology, high-performance circuits and devices, biological systems modeling like the brain and the heart, and decision making. The book is not only aimed at active researchers in the field of chaos control involving control and systems engineers, theoretical and experimental physicists, and applied mathematicians, but also at a general audience in related fields.

Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology
Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology

Author: Hamid R Arabnia

Publisher: Morgan Kaufmann

Published: 2015-08-11

Total Pages: 670

ISBN-13: 0128026464

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Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology discusses the latest developments in all aspects of computational biology, bioinformatics, and systems biology and the application of data-analytics and algorithms, mathematical modeling, and simu- lation techniques. • Discusses the development and application of data-analytical and theoretical methods, mathematical modeling, and computational simulation techniques to the study of biological and behavioral systems, including applications in cancer research, computational intelligence and drug design, high-performance computing, and biology, as well as cloud and grid computing for the storage and access of big data sets. • Presents a systematic approach for storing, retrieving, organizing, and analyzing biological data using software tools with applications to general principles of DNA/RNA structure, bioinformatics and applications, genomes, protein structure, and modeling and classification, as well as microarray analysis. • Provides a systems biology perspective, including general guidelines and techniques for obtaining, integrating, and analyzing complex data sets from multiple experimental sources using computational tools and software. Topics covered include phenomics, genomics, epigenomics/epigenetics, metabolomics, cell cycle and checkpoint control, and systems biology and vaccination research. • Explains how to effectively harness the power of Big Data tools when data sets are so large and complex that it is difficult to process them using conventional database management systems or traditional data processing applications. - Discusses the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological and behavioral systems. - Presents a systematic approach for storing, retrieving, organizing and analyzing biological data using software tools with applications. - Provides a systems biology perspective including general guidelines and techniques for obtaining, integrating and analyzing complex data sets from multiple experimental sources using computational tools and software.

Dynamical Chaos
Dynamical Chaos

Author: Vadim Semenovich Anishchenko

Publisher: World Scientific

Published: 1995

Total Pages: 410

ISBN-13: 9789810221423

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In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.