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Author: E. Atlee Jackson
Publisher: CUP Archive
ISBN: 9780521426329
Category : Mathematics
Languages : en
Pages : 532
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Book Description
The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Author: E. Atlee Jackson
Publisher: CUP Archive
ISBN: 9780521426329
Category : Mathematics
Languages : en
Pages : 532
Get Book Here
Book Description
The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Author: Marco Thiel
Publisher: Springer
ISBN: 3642046290
Category : Science
Languages : en
Pages : 300
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Book Description
This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author: Mark Shelhamer
Publisher: World Scientific
ISBN: 9812700293
Category : Science
Languages : en
Pages : 367
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Book Description
This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from physiologists to bioengineer.Initial chapters present background material on dynamic systems, statistics, and linear system analysis. Each computational technique is demonstrated with examples drawn from physiology, and several chapters present case studies from oculomotor control, neuroscience, cardiology, psychology, and epidemiology. Throughout the text, historical notes give a sense of the development of the field and provide a perspective on how the techniques were developed and where they might lead. The overall approach is based largely on the analysis of trajectories in the state space, with emphasis on time-delay reconstruction of state-space trajectories. The goal of the book is to enable readers to apply these methods to their own research.
Author: E. Atlee Jackson
Publisher: CUP Archive
ISBN: 9780521426336
Category : Mathematics
Languages : en
Pages : 676
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Book Description
The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
Author: J. M. T. Thompson
Publisher: John Wiley & Sons
ISBN: 9780471876847
Category : Science
Languages : en
Pages : 492
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Book Description
Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Author: Anne Beuter
Publisher: Springer Science & Business Media
ISBN: 0387216405
Category : Mathematics
Languages : en
Pages : 452
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Book Description
Introduces concepts from nonlinear dynamics using an almost exclusively biological setting for motivation, and includes examples of how these concepts are used in experimental investigations of biological and physiological systems. One novel feature of the book is the inclusion of classroom-tested computer exercises. This book will appeal to students and researchers working in the natural and physical sciences wanting to learn about physiological systems from a mathematical perspective.
Author: Edwin Atlee Jackson
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages :
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Book Description
Author: Richard Hollis Day
Publisher: Oxford University Press, USA
ISBN:
Category : Business & Economics
Languages : en
Pages : 360
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Book Description
Advances in physics, computers, and mathematics have made it possible to illustrate an astonishing array of potential behavior that can occur when nonlinear interactions are present. As Prigogine explains from a physicist's perspective, the fundamental role of instability and bounded rationality provide more precise understanding for evolution and changes. This volume considers these developments from various fields in the context of economic science. The work starts with a general non-mathematical discussion, introducing the major themes--nonlinearity, dynamical systems, and evolution in economic processes. The work continues with nonlinear analysis of macroeconomic growth and fluctuations. It describes analyses of economic adaptation, learning, and self-organization. The volume also scrutinizes a specific market--equities using nonlinear analysis, controlled experiments, and statistical inference when nonlinearity plays an essential role in data generation. The volume closes with an historical reflection by Richard Goodwin and a roundtable discussion on basic issues and new challenges in nonlinear economic dynamics.
Author: Leon O. Chua
Publisher: World Scientific Publishing Company
ISBN: 9789814390514
Category : Cellular automata
Languages : en
Pages : 0
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Book Description
When not immersed in science, he relaxes by searching for Wagner's leitmotifs, musing over Kandinsky's chaos, and contemplating Wittgenstein's inner thoughts.This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss.Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules.But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine.
