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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Cellular Automata: Analysis and Applications
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Cellular Automata: Analysis and Applications
Karl-Peter Hadeler, Johannes Müller (Gebundene Ausgabe, Englisch)
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Beschreibung
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 dynamicsof infectious d Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
15.06.2017
Sprache
Englisch
EAN
9783319530420
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Karl-Peter Hadeler, Johannes Müller
Seitenanzahl
467
Auflage
1
Einbandart
Gebundene Ausgabe
Schlagwörter
cellular automata, classification of cellular automata, dynamics of cellular automata, applications of cellular automata, decision problems in cellular automata
Thema-Inhalt
GPFC - Kybernetik und Systemtheorie
PHU - Mathematische Physik
PSAX - DV-gestützte Biologie/Bioinformatik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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