Consider again the harvest of the fish population of Example, modeled by dP/dt = (1 − P/10)P − H(t), where the time is measured in months. In Example, the strategy called for a constant harvesting rate of 3 tons per month, but only during the months of January, February, and March, with no harvesting allowed in the remaining months of the year.
a) Suppose that the harvesting season is actually during March, April, and May. Use dfield6 to show the fate of an initial population of ten tons of fish that are harvested at a constant rate of 3 tons per month during harvesting season, but not at all during the remaining months of the year. Hint: See Exercise.
b) Show the fate of the population in part a) if the harvesting season is in November, December, and January of each year.
c) In part b), the fate of the fish population depends on the initial population of fish. Use dfield6 to estimate the critical initial condition that separates survival from extinction.
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