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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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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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7.9 Further Reading (Optional) » References and Additional Reading
Lotka-Volterra Equations: This is a standard topic in many differential equations texts, so there are quite a few good references to choose from:
- The wikipedia page on the Lotka-Volterra equations is quite clear and could be a good place to start.
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Barnes, Belinda, and Glenn Robert Fulford. Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. CRC Press, 2011. Chapter five has a nice discussion of the Lotka-Volterra equations and variants thereof.
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Berryman, Alan A. "The orgins and evolution of predator-prey theory." Ecology 73.5 (1992): 1530-1535. A short review article giving some of the history of the Lotka-Volterra equations. Also discusses the limits of the Lotka-Volterra approach to interacting populations. [pdf]