
Project Requirements
1. Biographical Information
Your project should contain biographical sketchs of the Alfred Lotka and Vito Volterrra. Include any relevant information concerning their work with the predator prey models.
2. Proportional Harvesting
The following is a list of some things that should be included. Note that a satisfactory report will include more than the listed items.
dx/dt = ax  bxy  qx 
dy/dy = cy + pxy  ry 
incorporate proportional harvesting into the predatorprey model. What does "proportional" mean in this context?
(i) Explain why the average value of y(t) is given by the expression
Your goal is to show that y_{avg} = (a  q)/b.
(ii) First show that (dx/dt) / x = a  q  by(t).
(iii) Now show that
(iv) Explain why
iv) Conclude that
Therefore,
3. Constant Rate Harvesting
Consider the predator  prey model with harvesting given below.
dx/dt = ax  bxy  q 
dy/dy = cy + pxy  r 
Discuss how this model differs from the proportional harvesting model. Your discussion should include, but not be limited to, the following:

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