HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 6: Phase Plane Analysis of Ordinary Dierential Equations
Instructions: Log onto Blackboard. Under Course documents and then Week 6
download the le pplane8.m and the corresponding manual pplane.pdf f
HC 399/MTH 399H
Introduction to Mathematical Ecology
Metapopulation Dynamics
Discussion of Metapopulation Dynamics by I. Hanski. Topics/Questions for discussion:
1. What is Levins denition of a metapopulation?
2. Discuss the concepts of persistence, extin
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 8: Parameter Identication: A Competition Model
Instructions: Log onto Blackboard. Under Course documents and then Week 8
download the le pid.zip from the Wednesday item. Save this le in a temporary
Graham Wilkinson
Lab 7
Task 1
Task 2
A dt larger than about 0.286 is immediately unstable, giving very large results which cannot be shown
in the same plot as these stable versions.
Task 3
The solution becomes unacceptable at 1.0, but may return to reason
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 7: Solving Ordinary Dierential Equations in MATLAB
The ODE SUITE
The goal of this lab is to learn to use MATLABs built-in numerical solvers to nd
approximate solutions to a system of dierential equa
f function output = pplane8(action,input1,input2,input3) % pplane8 is an interactive tool for studying planar autonomous systems of % differential equations. When pplane8 is executed, a pplane8 Setup % window is opened. The user may enter the differential
7.
Introduction to PPLANE6
A planar system is a system of differential equations of the form
x =f (t, x, y),
y =g(t, x, y).
(7.1)
The variable t in system (7.1) usually represents time and is called the independent variable. Frequently,
the right-hand sid
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 5: Qualitative Analysis of Dierential Equations
Direction Fields and Phase Portraits
Instructions: Log onto Blackboard. Under Course documents and then Week 5
download the le deld8.m and the corresp
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 4: Simulating Systems of Discrete Equations
Nullclines, Equilibria, Phase Portraits and Time Series Plots
Goal: To study the behavior of systems of discrete equations called Host Parasitoid
Models.
15 Oct 09 - McEvoy. Exploring the Nicholson Bailey Model using Mathcad 8 - Based on Hassell's
'Spatial and Temporal Dynamics of Host-Parasitoid Interactions' Chapter 2
Coupled host-parasitoid interactions with discrete generations are often represented by
Task A.
1.
4
2.
3
3.
[1;3]
4.
[-0.7071 ; 0.7071] = [-1/sqrt(2); 1/sqrt(2)]
Task B
Answer is recorded as zero because the values became smaller than machine epsilon and cannot be stored.
The : operator allows an entire row or column to be accessed at o
Graham Wilkinson
Lab 3
Task A.
1. 4
2. 3
3. [1;3]
4.
[-0.7071 ; 0.7071] = [-1/sqrt(2); 1/sqrt(2)]
Task B
Answer is recorded as zero because the values became smaller than machine epsilon and cannot be
stored.
The : operator allows an entire row or column
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 3: Simulating Leslie Matrix Models
Eigenvalues, Eigenvectors, and Stable Age Distributions
Instructions: Log onto Blackboard. Under Course documents and then Week
3, in the Wednesday item download t
HC 399/MTH 399H
Introduction to Mathematical Ecology
Lab 2: Simulating Discrete Equations
Equilibria, Cobwebbing, and Bifurcation Diagrams
Instructions: Log onto Blackboard. Under Course documents and then Week 2,
in the Wednesday item download the zip le
HC 399/MTH 399H
Introduction to Mathematical Ecology
Week 1: Introduction to Modeling in Ecology
Discussion of An Introduction to the Practice of Ecological Modeling by Jackson et.
al. Topics/Questions for discussion:
1. What is a model?
2. What is a conc
HC 399/MTH 399H
Introduction to Mathematical Ecology
Final Group Project Description
Selection of the Final Project
For the Final project each group should pick a topic either from among the choices that are
oered in this document or from other sources. I