Final exam:
Look at all questions for the models in lab and on the homework assignments. In addiditon, the following are some items to consider:
Lotka Volterra:
What was the effect on the population graph of increasing the initial number of predators when the populations showed cycles?
Is this what you would have expected?
What happened to the minimum prey value when the initial number of prey was increased?
Logistic Equation
When the intrinsic rate, r, varies from 3 to 3.6 the output varies its oscillation pattern showing chaos, where the period for exact repetiton doubles during the transition from one behavior to the next. Past about 3.57, the output is no longer periodic and is unpredictable. This sort of behavior was first noticed by Konrad Lorentz in his meteorology models.
Daisy world Thought Questions in the link.
Traffic Model, Flocking, Life
Traffic Model questions in the link.
Focus on the the collective pattern of behavior resulting from simple rules for behavior of individuals. Resulting pattern not always predictable from the rules for individuals.
Yellow Fever Model
Look at the questions with the model.
Be familiar with the SIR model of infections.
Percolation Theory
This model shows how an oil spill can percolate down through permeable soil. It was inspired by a similar model meant to be done by hand on paper (see "Forest Fires, Oil Spills, and Fractal
Geometry", Mathematics Teacher, Nov. 1998, p. 684-5).
HOW IT WORKS?
The soil is modeled as a checkerboard of hard particles (gray squares) and semi-permeable spaces in between these hard particles (brown squares).
(You may need to zoom in to see the individual squares.)
Oil cannot enter the solid gray squares, but it may pass through the brown squares.
Some soils are more porous ("holey") than other soils.
In this model the porosity value of the soil determines the probability that the oil will be able to enter any given brown soil square.

The model represents an oil spill as a finite number of oil "particles", or simply oil drops.
The oil spill starts at the top of the view, and percolates downward.
The leading edge of the oil spill is represented by red squares, and every square that oil has passed through (or "saturated") is shown as black.
The oil drops sink downward through the soil by moving diagonally to the right or left, slipping between the hard gray particles.
This has become a general model of interest in a number of applications, anyhting which can be modeled with a probability-governed flow from one space to the neighboring spaces.
It can even serve as a simplified infection model involving the spread of disease through space as well as time.
Carbon Cycle Models
The questions in the Stella Carbon Cycle link.
What were the otcomes from the rainforest deforestation model and the biofuels model? How much of an effect did the models predict for the scenarios investigated?
IPCC model
8.7.1 Introduction This discussion of thresholds and abrupt climate change can be related to the discussion of the chemical titration when the region of control or buffer region is passed and the pH changes rapidly.
Notice that the discussion of model testing is in terms of estimating stocks and determining connections or flows, some of which we have only a limited understanding of. Sensitivity of the models to the estimates of these parameters compared to the uncertainty of our estimates is one key factor in how reliable the models’ predictions are.
Revisit the Borneo discussion from the first week and think about the
Law of Unintended Consequences . You should find at least 2 examples of this in the models we have dealt with.