Bifurcations introduction
Problem 1a (from IODE)
After allowing their fish hatchery equilibrated at 25000 fish (without any harvesting), the owners of fish.net have decided to allow harvesting based on the model . In this model, P is the number of fish in thousands, and k is a harvesting rate measured in thousands of fish per year. They initially allow a harvesting rate k = 12. If they allow fishing to continue for a while at this rate, what does their model predict for the long term number of fish in the lake?
Problem 1b
The early years of fish harvesting went well, so they increased the harvesting rate by a modest amount. They now allow harvesting rate corresponding to k = 13. What does this model predict will be the long term result of this fishing practice?
Problem 1c
The owners of fish.net panicked when their fish population reached P = 5 and decided to return to their original business model with k = 12. Will the fish population return to the levels you described in problem 1a? Why or why not?