This guided activity is comprised of three parts. Part 1 (Instruction) walks you through an example. Part 2 (Independent Practice) is where you will take what you
have learned in the example and apply it to your own chosen scenario. Finally, in Part 3 (Analysis), you will analyze your findings based on specific questions in
the prompt. You will complete Parts 2 and 3 and submit to your instructor. Each assignment builds upon what you have done before, so it is imperative that you
complete each assignment. The guided activities will be submitted in each module.
Part 2 (Independent Practice)
Verify the stability of the other equilibrium points that we found in Module Two. Please keep this in mind as we move forward into the next module, where we
discuss the phase portraits associated. For a refresher on linear algebra, perform at least one set of the calculations by hand. Set up the Jacobian Matrix, find the
partial derivatives, and do the calculations for one set of equilibrium points. For the balance, feel free to either do them by hand or use Sage.
Part 3 (Analysis)
We know less about the interactions between the two species than any other interaction. In Module Two, you determined at what level the interaction between
the two species became severe enough that they could not coexist. Determine the equilibrium points for this interaction level, and test their stability using the
eigenvalue method. You can do this either by hand or using Sage.