

Part 3.1: Competing Species I
Now we will look at a system of equations that is very similar to the predatorprey system. Indeed the only difference is a change in sign of some of the coefficients.
dx/dt = ax  bxy
dy/dt = cy  pxy
We still assume that a, b, c, and p are positive constants.
Let (x_{0},y_{0}) be the equilibrium point for the general system
The lines x = x_{0} and y = y_{0} divide the first quadrant in the xyplane into four subregions as indicated below.
For each subregion indicate whether x is increasing or decreasing and whether y is increasing or decreasing.
(b) Does this seem reasonable in terms of the biological population description you gave in Step 1? Explain why or why not.
(b) How do the trajectories of solutions to the system change as you vary the ratio a/c? Does this seem reasonable in terms of the biological population description you gave in Step 1? Explain why or why not.


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