Reality Rules, the Fundamentals

Volume 1 Auflage
ISBN: 978-0-471-18435-5
Verlag: Wiley

Buch, Englisch, 416 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 771 g

Die beiden ursprünglich 1992 veröffentlichten Bände liegen nun in zusammengefaßter Paperback-Form vor. Reality Rules beleuchten die Syntax und die Semantik der Sprache, in der mathematische Modellierungsregeln niedergelegt werden. Eine Vielzahl von Beispielen zeigt praktische Anwendungen auf; auch ein Lösungsband zur Unterstützung des Selbststudiums ist erhältlich.

Autoren/Hrsg.

Casti, John

Inhaltsverzeichnis

Aus dem Inhalt:

VOLUME 1: THE WAYS OF MODELMAKING: Natural Systems and Formal Mathematical Representations;
CATASTROPHES, DYNAMICS AND LIFE: The Singularities of Ecological and Natural Resource Systems;
PATTERN AND THE EMERGENCE OF LIVING FORMS: Cellular Automata and Discrete Dynamics;
ORDER IN CHAOS: Variety and Pattern in the Flow of Fluids, Populations and Money.
VOLUME 2: STRATEGIES FOR SURVIVAL: Competition, games and the Theory of Evolution;
THE ANALYTICAL ENGINE: A System-Theoretic View of Brains, Minds and Mechanisms;
TAMING NATURE AND MAN: Control Anticipation and Adaptation in Social and Biological Processes;
THE GEOMETRY OF HUMAN AFFAIRS: Connective Structure in Art, Literature and Games of Chance;
THE MYSTIQUE OF MECHANISMS: Computation, Complexity and the Limits to Reason;
HOW DO WE KNOW?: Myths, Models and Paradigms in the Creation of Beliefs.

Chapter One THE WAYS OF MODELMAKING: NATURAL SYSTEMS AND FORMAL MATHEMATICAL REPRESENTATIONS

1. A Theory of Models 1

2. States, Observables and Natural Systems 4
3. Equations of State 7

4. Equivalent Descriptions and the Fundamental Question of Modeling 10
5. Bifurcations and Catastrophes 17
6. Complexity 21
7. Error and Surprise 23
8. Formal Systems 25
9. Modeling Relations 28
Discussion Questions 35
Problems 40

Notes and References 44

Chapter Two CATASTROPHES, DENAMICS AND LIFE: THE SINGULARITIES OF ECOLOGICAL AND NATURAL RESOURCE SYSTEMS

1. The Classification Problem 53
2. Smooth Functions and Critical Points 57
3. Structural Stability and Genericity 60
4. Morse's Lemma and Theorem 66
5. The Splitting Lemma and Corank 70
6. Determinacy and Codimension 71
7. Unfoldings 74
8. The Thom Classification Theorem 78
9. Electric Power Generation 81
10. Bifurcations and Catastrophes 83
11. Harvesting Processes 87
12. estimation of Catastrophe Controversy 99

13. Forest Insect Pest Control 95
14. The Catastrophe Controversy 99
15. Mappings 103
16. Dynamical Systems, Flows and Attractors 107
17. Bifurcation of Vector Fields 114
18. Stochastic Stability and the Classification of Vector Fields 120
Discussion Questions 125
Problems 136
Notes and References 149

Chapter Three PATTERN AND THE EMERGENCE OF LIVING FORMS: CELLULAR AUTOMATA AND DISCRETE DYNAMICS

1. Discrete Dynamical Systems 161
2. Cellular Automata: The Basics 164
3. One-Dimensional Cellular Automata 170
4. Local Properties of One-Dimensional Automata 178
5. Global Properties of One-Dimensional Automata 182
6. Algebraic Properties of Additive Cellular Automata 186
7 Languages: Formal and Natural 189
8. DNA Sequences and Cellular Automata 195
9. L-Systems and the Growth of Plants 200
10. The Game of Life 203
11. A Cellular Automaton Model of Vertebrate Skin 209
12. Self-Reproducing Automata 211
13. Artificial Life 216
14. Cellular Automata-Extensions and Genera 222
Discussion Questions 224
Problems 234
Notes and References 241

Chapter Four ORDER IN CHAOS: VARIETY AND PATTERN IN THE FLOW OF FLUIDS, POPULATIONS AND MONEY

1. The Circle-10 System 250
2. Deterministic Mechanisms and Stochastic Behavior 255
3. Quasi-periodic Trajectories and the KAM Theorem 259
4. A Philosophical Digression. Randomness and Determinism in Dynamical System Modeling 263
5. Scalar Maps and the Period-3" Theorem 267
6. Snap-Back Repellors and Multi-Dimensional Chaos 272
7. Tests for Chaos 275
8. Economic Chaos 288

9. Beer, Bears, Bulls and Chaos 293
10. Population Fluctuations 304
11. Continuous Chaos and the Lorenz Attractor 306
12. Poincare Maps and Strange Attractors 310
13. Chaos and the Problem of Turbulence 318
14. Turbulent Behavior in the Spread of Disease 323
15. Self-Similarity and Fractals 326
16. Fractals and Domains of Attraction 335
Discussion Questions 340
Problems 345
Notes and References 358
Index 373

Über Autor(innen)

John L. Casti is a member of the faculty of the Santa Fe Institute and a professor at the Technical University of Vienna. He is the author of Alternate Realities, Paradigms Lost, Searching for Certainty, Complexification, and Five Golden Rules. Dr. Casti is the executive editor of Complexity, a journal published by John Wiley.