Practical Numerical Algorithms for Chaotic Systems
Title | Practical Numerical Algorithms for Chaotic Systems PDF eBook |
Author | Thomas S Parker |
Publisher | |
Pages | 368 |
Release | 1989-08-01 |
Genre | |
ISBN | 9781461234876 |
Practical Numerical Algorithms for Chaotic Systems
Title | Practical Numerical Algorithms for Chaotic Systems PDF eBook |
Author | Thomas S. Parker |
Publisher | Springer Science & Business Media |
Pages | 354 |
Release | 2012-12-06 |
Genre | Science |
ISBN | 1461234867 |
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
Title | Construction of Arithmetical Meanings and Strategies PDF eBook |
Author | Leslie Steffe |
Publisher | Springer |
Pages | 343 |
Release | 1987-12-18 |
Genre | Psychology |
ISBN | 9780387966885 |
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).
Pratical numerical Algorithms for chaotic systems
Title | Pratical numerical Algorithms for chaotic systems PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 1989 |
Genre | |
ISBN |
Practical Bifurcation and Stability Analysis
Title | Practical Bifurcation and Stability Analysis PDF eBook |
Author | Rüdiger Seydel |
Publisher | Springer Science & Business Media |
Pages | 493 |
Release | 2009-12-14 |
Genre | Mathematics |
ISBN | 144191739X |
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
Title | Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and Their Electronic Realization PDF eBook |
Author | Esteban Tlelo-Cuautle |
Publisher | CRC Press |
Pages | 266 |
Release | 2021 |
Genre | Chaotic behavior in systems |
ISBN | 9780367486686 |
"CRC Press is an imprint of the Taylor & Francis Group, an Informa business."
Dimensions and Entropies in Chaotic Systems
Title | Dimensions and Entropies in Chaotic Systems PDF eBook |
Author | Gottfried Mayer-Kress |
Publisher | Springer Science & Business Media |
Pages | 264 |
Release | 2012-12-06 |
Genre | Science |
ISBN | 3642710018 |
These proceedings contain the papers contributed to the International Work shop on "Dimensions and Entropies in Chaotic Systems" at the Pecos River Conference Center on the Pecos River Ranch in Spetember 1985. The work shop was held by the Center for Nonlinear Studies of the Los Alamos National Laboratory. At the Center for Nonlinear Studies the investigation of chaotic dynamics and especially the quantification of complex behavior has a long tradition. In spite of some remarkable successes, there are fundamental, as well as nu merical, problems involved in the practical realization of these algorithms. This has led to a series of publications in which modifications and improve ments of the original methods have been proposed. At present there exists a growing number of competing dimension algorithms but no comprehensive review explaining how they are related. Further, in actual experimental ap plications, rather than a precise algorithm, one finds frequent use of "rules of thumb" together with error estimates which, in many cases, appear to be far too optimistic. Also it seems that questions like "What is the maximal dimension of an attractor that one can measure with a given number of data points and a given experimental resolution?" have still not been answered in a satisfactory manner for general cases.