Refining and Optimizing Analytical Models
This section gives an example of how the model developed earlier could be extended to account for additional knowledge of the system's structure. Again, if you have not yet been exposed to this particular type of mathematical analysis, simply note that all models can be refined as we gain more knowledge about the system. Think back to the model you identified in the last section. How could you extend this model to make it a better reflection of reality?
Interaction (Euler's method for Systems)
Interaction Validation
Validation
The problem was
A client of the fish farm wants an aquarium with 20 rainbowfish, and 5 gouramis. Is it possible to have both fish in the same aquarium without one of them going extinct?
After constructing a mathematical model (for which the numbers are admittedly soso), graphs of the resulting solutions for both populations are
So the number of rainbowfish will grow fast from the initial 20 to about 55 in the first week. Because of the plentyfull rainbowfish, the number of gouramis will triple in a week and a half. The gouramis will eat more and more of the rainbowfish, so the number of rainbowfish will decrease again to about 25 after two weeks. With fewer rainbowfish, the number of gouramis decreases again, giving the rainbowfish population the chance to grow again. And so on, and so on. The increases and decreases of both populations become smaller in time, and after a month and a half, both populations stabilize to approximately 31 rainbowfish and 12 gouramis.