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An Introduction to Sequential Dynamical Systems

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An Introduction to Sequential Dynamical Systems Cover

 

Synopses & Reviews

Publisher Comments:

Sequential Dynamical Systems (SDS) are a class of discrete dynamical systems which significantly generalize many aspects of systems such as cellular automata, and provide a framework for studying dynamical processes over graphs. This text is the first to provide a comprehensive introduction to SDS. Driven by numerous examples and thought-provoking problems, the presentation offers good foundational material on finite discrete dynamical systems which leads systematically to an introduction of SDS. Techniques from combinatorics, algebra and graph theory are used to study a broad range of topics, including reversibility, the structure of fixed points and periodic orbits, equivalence, morphisms and reduction. Unlike other books that concentrate on determining the structure of various networks, this book investigates the dynamics over these networks by focusing on how the underlying graph structure influences the properties of the associated dynamical system. This book is aimed at graduate students and researchers in discrete mathematics, dynamical systems theory, theoretical computer science, and systems engineering who are interested in analysis and modeling of network dynamics as well as their computer simulations. Prerequisites include knowledge of calculus and basic discrete mathematics. Some computer experience and familiarity with elementary differential equations and dynamical systems are helpful but not necessary.

Synopsis:

This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. SDSs are a class of discrete dynamical systems which are a significant generalization of cellular automata and provide a new general theory of discrete computer simulations. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory --- equivalence, fixed points, invertibility and other phase space properties --- thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications  in computer science are explored.

The applied mathematics/computer science graduate students taking courses in dynamical systems, theoretical computer science, computer simulation and network theory should have a good knowledge of calculus and some computer experience. Familiarity with  elementary differential equations or linear algebra is helpful but not necessary.

Synopsis:

This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Table of Contents

Preface.- What is a Sequential Dynamical System?- A Comparative Study.- Graphs, Groups, and Dynamical Systems.- Sequential Dynamical Systems over Permutations.- Phase-Space Structure of SDS and Special Systems.- Graphs, Groups, and SDS.- Combinatorics of Sequential Dynamical Systems over Words.- Outlook.- References.- Index.

Product Details

ISBN:
9780387306544
Author:
Mortveit, Henning S.
Publisher:
Springer
Author:
Reidys, Christian M.
Author:
Mortveit, Henning
Author:
Reidys, Christian
Subject:
Computer Science
Subject:
Differential Equations
Subject:
Applied
Subject:
Discrete Mathematics
Subject:
Mathematics-Differential Equations
Subject:
Mathematical Analysis
Subject:
Dynamical Systems and Ergodic Theory
Subject:
Simulation and Modeling
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Discrete Mathematics in Computer Science
Copyright:
Edition Number:
260
Edition Description:
Book
Series:
Universitext
Publication Date:
20071031
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
260
Dimensions:
235 x 155 mm 404 gr

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An Introduction to Sequential Dynamical Systems New Trade Paper
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Product details 260 pages Springer - English 9780387306544 Reviews:
"Synopsis" by , This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. SDSs are a class of discrete dynamical systems which are a significant generalization of cellular automata and provide a new general theory of discrete computer simulations. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory --- equivalence, fixed points, invertibility and other phase space properties --- thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications  in computer science are explored.

The applied mathematics/computer science graduate students taking courses in dynamical systems, theoretical computer science, computer simulation and network theory should have a good knowledge of calculus and some computer experience. Familiarity with  elementary differential equations or linear algebra is helpful but not necessary.

"Synopsis" by , This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
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