Chaos and Dynamical Systems

Name: Chaos and Dynamical Systems | Complexity and Order in Evolution and Thought
Brand: Princeton University Press
Price: 39.99 EUR
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Complexity and Order in Evolution and Thought

David P. Feldman(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 6. August 2019

264 Seiten

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978-0-691-18939-0 (ISBN)

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Inhalt

Cover
Contents
Preface
1. Introducing Iterated Functions
1.1 Iterated Functions
1.2 Thinking Globally
1.3 Stability: Attractors and Repellors
1.4 Another Example
1.5 One More Example
1.6 Determinism
1.7 Summary
2. Introducing Differential Equations
2.1 Newton's Law of Cooling
2.2 Exact Solutions
2.3 Calculus Puzzles
2.4 Qualitative Solutions
2.5 Numerical Solutions
2.6 Putting It All Together
2.7 More about Numerical Solutions
2.8 Notes on Terminology and Notation
2.9 Existence and Uniqueness of Solutions
2.10 Determinism and Differential Equations
2.11 Iterated Functions vs. Differential Equations
2.12 Further Reading
3. Interlude: Mathematical Models and the Newtonian Worldview
3.1 Why Isn't This the End of the Book?
3.2 Newton's Mechanistic World
3.3 Laplacian Determinism and the Aspirations of Science
3.4 Styles of Mathematical Models
3.5 Levels of Models
3.6 Pluralistic View of Mathematical Models
3.7 Further Reading
4. Chaos I: The Butterfly Effect
4.1 The Logistic Equation
4.2 Periodic Behavior
4.3 Aperiodic Behavior
4.4 The Butterfly Effect
4.5 The Butterfly Effect Defined
4.6 Chaos Defined
4.7 Lyapunov Exponents
5. Chaos II: Deterministic Randomness
5.1 Symbolic Dynamics
5.2 As Random as a Coin Toss
5.3 Deterministic Sources of Randomness
5.4 Implications of the Butterfly Effect
5.5 Further Reading
6. Bifurcations: Sudden Transitions
6.1 Logistic Differential Equation
6.2 Logistic Equation with Harvest
6.3 Bifurcations and Bifurcation Diagrams
6.4 General Remarks on Bifurcations
6.5 Catastrophes and Tipping Points
6.6 Hysteresis
6.7 Further Reading
7. Universality in Chaos
7.1 Logistic Equation Bifurcation Diagram
7.2 Exploring the Bifurcation Diagram
7.3 Some Words about Emergence
7.4 The Period-Doubling Route to Chaos
7.5 Universality in Maps
7.6 Universality in Physics
7.7 Renormalization
7.8 Phase Transitions, Critical Phenomena, and Power Laws
7.9 Conclusion: Lessons and Limits to Universality
7.10 Further Reading
8. Higher-Dimensional Systems and Phase Space
8.1 A Quick Review of One-Dimensional Differential Equations
8.2 Lotka-Volterra Differential Equations
8.3 The Phase Plane
8.4 Phase Planes in General
8.5 The Rössler Equations and Phase Space
8.6 Further Reading
9. Strange Attractors
9.1 Chaos in Three Dimensions
9.2 The Rössler Attractor
9.3 Strange Attractors
9.4 Back to 1D: The Lorenz Map
9.5 Stretching and Folding
9.6 Poincaré Maps
9.7 Delay Coordinates and Phase Space Reconstruction
9.8 Determinism vs. Noise
9.9 Further Reading
10. Conclusion
10.1 Summary
10.2 Complex Systems
10.3 Emergence(?)
10.4 But Not Everything Is Simple
10.5 Further Reading
10.6 Farewell
Bibliography
Index

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