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Universitext

An Introduction to Sequential Dynamical Systems

Authors: Mortveit, Henning, Reidys, Christian

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  • First graduate textbook on Sequential Dynamical Systems
  • Details seminal SDS research toward a general theory of discrete computer simulations, with applications developed in government labs
  • Versatile interdisciplinary textbook relevant to applied mathematicians and computer scientists alike
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-0-387-49879-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-0-387-30654-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

From the reviews:

"By a sequential dynamical system (SDS), Mortveit (Virginia Polytechnic Institute and State Univ.) and Reidys (Nankai Univ., China) mean a certain type of mathematical model. … Summing Up: Recommended. Upper-division undergraduate through professional collections." (D. V. Feldman, CHOICE, Vol. 45 (10), June, 2008)

"A comprehensive introduction to sequential dynamical systems (SDS), i.e. a class of dynamical systems defined over graphs where the dynamics arise through functional composition of local dynamics. … The book will be useful to graduate students and researches in discrete mathematics, dynamical systems, theoretical computer science, and systems engineering … ." (Georgy Osipenko, Zentralblatt MATH, Vol. 1135 (13), 2008)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • What is a Sequential Dynamical System?

    Pages 1-22

  • A Comparative Study

    Pages 23-37

  • Graphs, Groups, and Dynamical Systems

    Pages 39-67

  • Sequential Dynamical Systems over Permutations

    Pages 69-128

  • Phase-Space Structure of SDS and Special Systems

    Pages 129-163

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-0-387-49879-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-0-387-30654-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Sequential Dynamical Systems
Authors
Series Title
Universitext
Copyright
2008
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-49879-9
DOI
10.1007/978-0-387-49879-9
Softcover ISBN
978-0-387-30654-4
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 248
Number of Illustrations
73 b/w illustrations
Topics