Cellular automata : analysis and applications
- 作者： Hadeler, Karl-Peter, author.
- 其他作者：
- 其他題名：
- Springer monographs in mathematics.
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Springer monographs in mathematics,
- 主題： Cellular automata. , Mathematics. , Dynamical Systems and Ergodic Theory. , Complex Systems. , Mathematical Applications in the Physical Sciences. , Mathematical and Computational Biology.
- ISBN： 9783319530437 (electronic bk.) 、 9783319530420 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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 Kurka -- 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.
- 摘要註: 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 Cutis-Hedlund-Lyndon 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 (Kurka 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 self-similar 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 Bar-Yam model for Turing pattern, and Greenberg-Hastings automata for excitable media. Also models for sandpiles, the dynamics of infectious diseases and evolution of predator-prey
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讀者標籤：
- 系統號： 005399834 | 機讀編目格式
館藏資訊
This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult 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 to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various 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 that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question of whether the properties of cellular automata are decidable. Surjectivity and injectivity are examined, and the seminal Garden of Eden theorems are discussed. In turn, 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 us to define self-similar 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 Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media. In addition, models for sand piles, the dynamics of infectious d