In our analysis, we found that the equations for z'(t) and w'(t) could be decoupled from the first two equations and that the solutions to this uncoupled system was:

for lambda > 0 and that z(t) and w(t) decay as t increases for lambda < 0.

We also discovered that the origin acted as a source when lambda > 0 and c1 < 0 and as a sink when lambda < 0 and c1 > 0. When c1 and lambda have the same sign, interesting behavior occurs. In these cases, the origin acts as a saddle with four eigenvectors, two of which are stable. We also determined how varying the constants c1 and lambda affected the corresponding phase portraits.

The rest of this report is split into three sections: the background section describes the model. The results of our analysis are given in the third section as well as numerous calculations, graphs, and phase-portraits. Finally, the