Homework 4.1 (due Feb.9)
1. For the spruce budworm model from class: do the following:
a) Plot the Hamiltonian as a surface over (u, v)-plane, look at the projections
of the level curves and convince yourself that (0,0) is indeed a center.
b) Find the approximate steady state solution of the full PDE model by solving
the system of ODEs for D = 0.25, µ = 1, l = 2. To do this start with different
initial conditions for v, find the solution numerically, see what value of l that
gives and then modify the initial condition until you find a solution that has
the right value of l. Plot the PDE solution that you found as a function of x.
c) Repeat the process for a larger value of mu. How does the solution change
µ? Why? Give a biological (or intuitive, in words) explanation for why what
you observe should be the case.
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