Use the applet below to generate a phase diagram numerically using the baseline parameters. Copy the diagram from Problem 4 by hand, and supply the directions of motion in each isosector. For example, the arrow pointing northward in isosector II indicates increasing values of x over time. The arrow pointing eastward in isosector II indicates increasing values of y over time. The figure from Problem 4 is helpful in understanding the dynamics associated with various regions of the phase plane.
Growth rates are positive in both parcels since each population is below carrying capacity.
The social fence is open for forward migration from x to y since population levels are above the zero-dispersion line. Hence, x enjoys a positive growth rate, but suffers emigration losses. Initial levels of x above xi initially decrease over time because emigration is greater than growth each period. However, once the population falls below xi , the growth rate overwhelms the emigration rate, and the population begins to increase. Conversely, positive growth rates work together with immigration gains to increase y .