Consider a fish population with constant harvesting, modeled by the equation dP/dt = (1 − P/10)P − H. If there is no harvesting allowed, then the fish population behaves according to the logistic model (See Example in Chapter).
a) Enter the differential equation in the DFIELD6 Setup window. Add a parameter H and set it equal to zero. Use the Keyboard input box to sketch the equilibrium solutions. The equilibrium solutions divide the plane into three regions. Sketch one solution trajectory in each of the three regions.
b) Slowly increase the parameter H and note how the equilibrium solutions move closer together, eventually being replaced by one, then no equilibrium solutions. This is called a bifurcation and has great impact on the eventual fate of the fish population. Use dfield6 to experimentally determine the value of H at which this bifurcation takes place. Note: If you find it difficult to find the exact bifurcation point with dfield6, you might consider the graph of (1 − P/10)P − H versus P, as in Figure in Chapter. For what value of H does this plot have exactly one intercept? Check your response in dfield6.
c) Prepare a report on the effect of constant harvesting on this fish population. Your report should include printouts of the DFEELD6 Display window for values of H on each side of the bifurcation point and an explanation of what happens to the fish population for a variety of different initial conditions.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.