For the species X and Y in Exercises 27 and 28, suppose
Chapter , Problem 29(choose chapter or problem)
For the species X and Y in Exercises 27 and 28, suppose that X reproduces very quickly if it is on the island with no Ys present and that species Y reproduces slowly if there are no Xs present. Also suppose that the growth rate of species X is decreased a relatively large amount by the presence of Y but that species Y is indifferent to Xs population. (a) What can you say about f/x and g/y at (0, 0)? (b) What can you say about f/y and g/x at (0, 0)? (c) What are the possible type(s) for the equilibrium point at (0, 0)? [There may be more than one possibility. If so, specify all of them.] (d) For each of the types listed above, sketch the phase portrait near (0, 0). Be sure to justify all answers.
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