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Contents
Spatio-Temporal Models in Ecology; an Introduction to Integro-Difference Equations
James Powell
1
Department of Mathematics and Statistics
Utah State University
Contents
Lab 1 - Introducing M
ATLAB
Goals
Introducing the Software
Defining One-Dimensional Functions and Graphing
Scalar Functions of Two Variables
Basic Logical Functions
Learning about Matrix Manipulation and Fourier Transforms using the Demos
Lab 2 - Dispersal
Goals
Probability and Dispersal in One Space Dimension
Dispersal via Random Walks and the Diffusion Equation
Convolutions and Fourier Transforms
Numerical FFT
Matlab Implementation
Dispersal and Settling with a Localized Source
Ballistic Dispersal
Movement at Constant Speed from a Source and Settling
Probability and Dispersal in Two Space Dimensions
Dispersal via Random Walks in Two Dimensions
Modal Dispersal in Two Dimensions
Turchin's Model for Prey-Taxis
Lab 3 - Implementing an Integro-Difference Model
Goals
Enhanced Nicholson-Bailey Model
Matlab Implementation of the Simplest IDE
An Integro-Difference Approach to Nicholson-Bailey
Description of IDE for ENB
Matlab Implementation
Spatially Structured Environments
Lab 4 - Boundaries, Chemotaxis and Student Case Studies
Goals
Reflecting and Absorbing Boundary Conditions
The Wall of Doom
Reflecting Boundaries
Mixed Boundaries
Boundary Conditions in Two Dimensions
A Model for Chemo-Taxis
Bibliography
James Powell
2001-04-06
