-
-
Welcome and Course Overview
-
How to Take this Course
-
Introduction to Functions
-
Iteration
-
Fixed Points and Stability
-
Summary
-
Homework (Optional)
-
Homework Solutions (Optional)
-
Test
-
-
-
Introduction
-
The Idea of the Derivative
-
Differential Equations
-
Computational Solutions
-
Qualitative Solutions
-
Summary
-
Newton, Laplace, and Determinism
-
Homework (Optional)
-
Test
-
-
-
Introducing the Logistic Equation
-
Iterating the Logistic Equation
-
The Butterfly Effect
-
Randomness?
-
Modeling Styles
-
Lyapunov Exponents (Optional)
-
Logistic Equation Programs
-
Summary
-
Homework (Optional)
-
Test
-
-
-
The Logistic Differential Equation
-
Logistic Equation with Harvest
-
Bifurcation Diagrams
-
Bifurcations
-
Hysteresis (Optional)
-
Summary
-
Homework (Optional)
-
Test
-
-
-
Final State Diagrams
-
The Bifurcation Diagram
-
Bifurcation Diagram Explorations
-
Logistic Equation Programs
-
Summary
-
Homework (Optional)
-
Test
-
-
-
Introduction
-
Universality in Maps
-
Universality in Physical Systems
-
Renormalization
-
Summary
-
Bifurcation Diagram Programs
-
Homework (Optional)
-
Further Reading (Optional)
-
Test
-
-
-
Lotka Volterra Differential Equations
-
The Phase Plane
-
The Hénon Map
-
The Lorenz Equations
-
Summary
-
Hénon Map Program
-
Homework (Optional)
-
Test
-
Further Reading (Optional)
-
-
-
The Hénon Attractor
-
The Lorenz Attractor
-
Stretching and Folding
-
Links to Programs
-
Summary
-
Homework (Optional)
-
Test
-
-
-
Diffusion
-
Reaction-Diffusion Equations
-
Computer Experiments
-
Real Experiments
-
Summary
-
Links to Programs
-
Additional Resources (Optional)
-
No Homework for Unit 9
-
No Test for Unit 9
-
-
-
Summary and Overview
-
Interview: Stephen H. Kellert
-
Interview: Stephen W. Morris
-
Themes and Conclusions
-
Farewell
-
3.3 The Butterfly Effect » Video 5 (7:25) Download Video Subtitles & Transcripts Slides for this lecture
Slides for this lecture
Robert C. Hilborn, Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics. American Journal of Physics. 72(4):425. 2004.
Subtitles are available in the following languages:
- N/A
If subtitles are available for a given video they can be accessed in the following way. First, start and pause the video. A tool bar will now be visible along the bottom of the video. Second, click on the gear-shaped button located directly to the right of the “CC” button. A list of available languages will be shown in the middle drop-down menu located in the box the opens after hitting the gear-shaped button. Select the language you would like to use for subtitles and click on it.