

Part 2.4: Equilibrium Points
Use the applet to experiment with trajectories for a predatorprey system, notice that there seems to be one set of initial conditions for which the trajectory consists of a single point. At such a point neither population function changes; they are in equilibrium. For this reason such a point is said to be an equilibrium point.
dx/dt = ax  bxy
dy/dt = cy + pxy
(b) Use the result in (a) to calculate the coordinates of the equilibrium point for the system with the coefficient values a =1, b = 0.03, c = 0.4, and p = 0.01 . Compare the results of this calculation with your calculation in Step 1.
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) How does the pattern of trajectories change as the coefficient changes?
(c) Do the changes noted in (a) and (b) agree with your intuition about predatorprey interactions?


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