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Welcome and Course Overview
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How to Take this Course
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Introduction to Functions
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Iteration
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Fixed Points and Stability
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Summary
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Homework (Optional)
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Homework Solutions (Optional)
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Test
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Introduction
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The Idea of the Derivative
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Differential Equations
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Qualitative Solutions
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Computational Solutions
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Summary
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Newton, Laplace, and Determinism
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Homework (Optional)
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Test
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Introducing the Logistic Equation
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Iterating the Logistic Equation
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The Butterfly Effect
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Randomness?
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Modeling Styles
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Lyapunov Exponents (Optional)
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Logistic Equation Programs
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Summary
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Homework (Optional)
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Test
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The Logistic Differential Equation
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Logistic Equation with Harvest
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Bifurcation Diagrams
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Bifurcations
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Hysteresis (Optional)
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Summary
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Homework (Optional)
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Test
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Final State Diagrams
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The Bifurcation Diagram
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Bifurcation Diagram Explorations
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Logistic Equation Programs
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Summary
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Homework (Optional)
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Test
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Introduction
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Universality in Maps
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Universality in Physical Systems
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Renormalization
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Summary
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Bifurcation Diagram Programs
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Homework (Optional)
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Further Reading (Optional)
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Test
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Lotka Volterra Differential Equations
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The Phase Plane
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The Hénon Map
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The Lorenz Equations
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Summary
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Hénon Map Program
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Homework (Optional)
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Test
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Further Reading (Optional)
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The Hénon Attractor
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The Lorenz Attractor
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Stretching and Folding
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Links to Programs
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Summary
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Homework (Optional)
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Test
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Diffusion
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Reaction-Diffusion Equations
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Computer Experiments
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Real Experiments
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Summary
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Links to Programs
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Additional Resources (Optional)
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No Homework for Unit 9
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No Test for Unit 9
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Summary and Overview
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Interview: Stephen H. Kellert
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Interview: Stephen W. Morris
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Themes and Conclusions
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Farewell
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5.4 Logistic Equation Programs » Links to Programs
I put links to the logistic programs so you can find them easily when you are working on a quiz or the homework.
- Click here for the program calculate orbits for the logistic equation and display the timeseries plot.
- Click here for the program that will calculate the orbits for two different initial conditions, show their time series plots, and also plot the difference between the two orbits.
- Click here for a program that will plot a bifurcation diagram.
Here is a zip file containing all the files needed to run all threeprograms on your own computer. Make a folder on your computer and download the zip file into it. Then unzip the file. The three files to open are time_series.html, initial_conditions.html, and bifurcation.html. Open these in your favorite web browser, and you should be able run the programs in your browser. If you encounter problems, please let one of us know or post a query on the forum. It is possible that these instructions will need be modified slightly for different operating systems.