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The Resource Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource)
Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource)
Resource Information
The item Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental CutisHedlundLyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification). These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define selfsimilar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the BarYam model for Turing pattern, and GreenbergHastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predatorprey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit
 Language
 eng
 Extent
 XI, 467 p. 78 illus., 3 illus. in color.
 Contents

 1.Introduction
 2.Cellular automata  basic definitions
 3.Cantor topology of cellular automata
 4.Besicovitch and Weyl topologies
 5 Attractors
 6 Chaos and Lyapunov stability
 7 Language classification of Kůrka
 8.Turing machines, tiles, and computability
 9 Surjectivity and injectivity of global maps
 10.Linear Cellular Automata
 11 Particle motion
 12
 Pattern formation
 13.Applications in various areas
 A.Basic mathematical tools
 Isbn
 9783319530437
 Label
 Cellular Automata: Analysis and Applications
 Title
 Cellular Automata: Analysis and Applications
 Statement of responsibility
 by KarlPeter Hadeler, Johannes Müller
 Subject

 Complex Systems
 Biomathematics
 Biomathematics
 Mathematical physics
 Mathematical physics
 Dynamics
 Dynamics
 System theory
 Electronic resources
 Mathematics
 Mathematical and Computational Biology
 System theory
 Ergodic theory
 Mathematical Applications in the Physical Sciences
 Mathematics
 Dynamical Systems and Ergodic Theory
 Ergodic theory
 Language
 eng
 Summary
 This book focuses on a coherent representation of the main approaches to analyze the dynamics of cellular automata. Cellular automata are an inevitable tool in mathematical modeling. In contrast to classical modeling approaches as partial differential equations, cellular automata are straightforward to simulate but hard to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction of cellular automata on Cayley graphs, and their characterization via the fundamental CutisHedlundLyndon theorems in the context of different topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification). These classifications suggest to cluster cellular automata, similar to the classification of partial differential equations in hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question, whether properties of cellular automata are decidable. Surjectivity, and injectivity are examined, and the seminal Garden of Eden theorems are discussed. The third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows to define selfsimilar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the BarYam model for Turing pattern, and GreenbergHastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predatorprey systems are discussed. Mathematicians find an overview about theory and tools for the analysis of cellular automata. The book contains an appendix introducing basic mathematical techniques and notations, such that also physicists, chemists and biologists interested in cellular automata beyond pure simulations will benefit
 http://library.link/vocab/creatorName
 Hadeler, KarlPeter
 Image bit depth
 0
 LC call number
 QA313
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Müller, Johannes.
 SpringerLink
 Series statement
 Springer Monographs in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Dynamics
 Ergodic theory
 System theory
 Mathematical physics
 Biomathematics
 Mathematics
 Dynamical Systems and Ergodic Theory
 Complex Systems
 Mathematical Applications in the Physical Sciences
 Mathematical and Computational Biology
 Label
 Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1.Introduction  2.Cellular automata  basic definitions  3.Cantor topology of cellular automata  4.Besicovitch and Weyl topologies  5 Attractors  6 Chaos and Lyapunov stability  7 Language classification of Kůrka  8.Turing machines, tiles, and computability  9 Surjectivity and injectivity of global maps  10.Linear Cellular Automata  11 Particle motion  12  Pattern formation  13.Applications in various areas  A.Basic mathematical tools
 Dimensions
 unknown
 Extent
 XI, 467 p. 78 illus., 3 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319530437
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319530437
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319530437
 Label
 Cellular Automata: Analysis and Applications, by KarlPeter Hadeler, Johannes Müller, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 1.Introduction  2.Cellular automata  basic definitions  3.Cantor topology of cellular automata  4.Besicovitch and Weyl topologies  5 Attractors  6 Chaos and Lyapunov stability  7 Language classification of Kůrka  8.Turing machines, tiles, and computability  9 Surjectivity and injectivity of global maps  10.Linear Cellular Automata  11 Particle motion  12  Pattern formation  13.Applications in various areas  A.Basic mathematical tools
 Dimensions
 unknown
 Extent
 XI, 467 p. 78 illus., 3 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319530437
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319530437
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319530437
Subject
 Biomathematics
 Biomathematics
 Complex Systems
 Dynamical Systems and Ergodic Theory
 Dynamics
 Dynamics
 Electronic resources
 Ergodic theory
 Ergodic theory
 Mathematical Applications in the Physical Sciences
 Mathematical and Computational Biology
 Mathematical physics
 Mathematical physics
 Mathematics
 Mathematics
 System theory
 System theory
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