Synopses & Reviews
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.
Review
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)
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.
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.
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.