Modellierung komplexer Prozesse durch naturanaloge by Christina Stoica-Klüver, Jürgen Klüver, Jörn Schmidt (auth.)

By Christina Stoica-Klüver, Jürgen Klüver, Jörn Schmidt (auth.)

Dieses Lehrbuch ist eine Einfuhrung in die Techniken des sog. tender Computing und verwandter formaler Methoden. Dargestellt werden Zellularautomaten und Boolesche Netze, Evolutionare Algorithmen sowie Simulated Annealing, Fuzzy-Methoden, Neuronale Netze und schlie?lich Hybride Systeme, d. h. Koppelungen verschiedener dieser Techniken. Zu jeder Technik werden Anwendungsbeispiele gegeben. Auf der foundation der Theorie komplexer dynamischer Systeme werden zusatzlich theoretische Grundlagen dargestellt und es wird auf die Gemeinsamkeiten der auf einen ersten Blick sehr heterogenen Techniken hingewiesen.
Der Leser erhalt eine systematische Einfuhrung und Ubersicht zu diesen Techniken. Durch die Beispiele wird er geschult, selbst in formalen Modellen zu denken und diese auf seine speziellen Probleme anzuwenden. Dieses Lehrbuch ist fur den Einsatz in Lehrveranstaltungen zur Simulation komplexer adaptiver Systeme sowie zur Modellbildung und -theorie in verschiedenen Bereichen geeignet.

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Extra info for Modellierung komplexer Prozesse durch naturanaloge Verfahren: Komplexe adaptive Systeme — Modellbildungen und -theorie — neuronale Netze — Soft Computing und verwandte Techniken

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Induktionsanfang). Anschließend folgt der sog. Induktionsschritt, indem man von der Annahme, dass man die Behauptung für ein beliebiges n bewiesen hat, zeigt, dass dann die Behauptung auch für n + 1 gilt. In der obigen Formel ist die Variable n übrigens so zu verstehen, dass für die übliche Moore-Umgebung gilt, dass n = 1; die Erweiterung ergibt dann n = 2 usf. 30 2. Zellularautomaten und Boolesche Netze Bild 2-3a Ein dreidimensionaler ZA nach 1 Schritt; „Falken“ sind grau, „Tauben“ schwarz. Bild 2-3b Ein dreidimensionaler ZA nach 10 Schritten Man kann jetzt auch die Anzahl der möglichen Regeln für den Fall angeben, dass die Anzahl der möglichen Zellenzustände n > 2 ist bei k Umgebungszellen.

Bei der Konstruktion oder Zufallsgenerierung einer W-Matrix muss darauf geachtet werden, dass die Zeilen in der Gesamtsumme immer 1 ergeben, da irgendein Übergang, und sei es auch der identische, immer stattfinden muss. : Die Summe der Übergangswahrscheinlichkeiten ergibt eine deterministische Gesamtsituation. Die Konstruktion einer W-Matrix ergibt sich aus dem Grundlegenden Prinzip der ZA, dass die lokalen Umgebungsregeln ja stets Übergangsregeln in Bezug auf die jeweiligen Zellenzustände sind.

Lauten dann: (1) (¦i < 3, 0), (¦i > 4, 0), (2) (¦i = 3, 1), (3) (¦i = 4, jt, jt). 2 wird ein stochastischer ZA (siehe unten) gezeigt, dessen totalistische Regeln mit der Bildung von Durchschnittswerten arbeiten. Dessen Regeln lassen sich u. a. 1) für jt > n. 6) Anders ausgedrückt, der Zustand der Zentralzelle nähert sich sukzessive dem Durchschnittszustand der Umgebungszellen an. Aus derartigen Darstellungen lässt sich eine Charakterisierung der Regeln eines spezifischen ZA ableiten, nämlich die sog.

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