I am attempting to solve the following problem:
Assuming an adult survival rate of 60% and a reproductive rate of 2/3 female chick per year, is there a juvenile survival rate at which the population stabilizes (with positive population)? Hint: A stable population corresponds to lambda=1 being the dominant eigenvalue.
I have already set up the matrix below. I think I have set the value of lambda=1 appropriately, however I am new to Mathematica and unsure. I need to utilize a Solve function to solve for the variable 'a'. However, I can't seem to find any examples of this particular type of problem.
Maybe this?
Eigenvalues[{{6/10, a}, {2/3, 0}}] Solve[%[[2]] == 1]
You can make an interactive simulation:
Manipulate[ DiscretePlot[ MatrixPower[{{6/10, a}, {2/3, 0}}, n] . {110, 30}, {n, 0, 10}, Joined -> True], {{a, 3/5}, 0, 1}]
