| Mathematics Problem:?
Whale population.
Consider the survival of a population of whales, and assume that if the number of whales falls below a minimum survival level m, then the species will become extinct. In addition, assume that the population is limited by the carrying capacity M of the environment. That is, if the whale population is above M, then it will experience a decline because the environment cannot sustain that large a population level.
- Let a_(n) represent the whale population after n years. Discuss the model
a_(n+1) = a_(n) + k{M - a_(n)}{a_(n) - m},
where k > 0. Does it make sense in terms of the description above?
- Find the fixed points of the model, and determine their stability via linearization. You may assume that M=5000, m=100, and k=0.0001.
- Perform a graphical stability analysis. Are your results consistent with the results from question above? | 
03-06-2008, 08:46 PM
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