X2 Applied Mathematics
Population models 2: Two Species
Symbiosis
Here the presence of bothe species is mutually beneficial. A simple attempt at modelling this could be to reverse the signs of b and c in the previous rabbit-sheep model:
Unfortunately such a model has an intrinsic problem that it can be possible for the populations to blow up to infinity in a finite time.
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Work through the exercise below and hand it in.
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Exercise: To see that the populations can blow up in a finite time take the problem with a=1, and b=c=2. Then assume that r=s (If this is initially so then it will remain true). Find an explicit solution for the population and show that it can go to infinity in a finite time.
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