Answer

The figure above shows the rough direction field or lake diagram. Notice that

• When the predator population p is less than 200 the prey population q increases and when the predator population is above 200 the prey population decreases.

• When the prey population q is below 200 then the predator population decreases and when the prey population is above 200 the predator population increases.

• There are two equilibrium points -- (0, 0) and (200, 200).

• In the absence of the predator population, the prey population would go off to infinity.

• in the absence of the prey population, the predator population would die out.

• The currents are "swirling around" the equilibrium point (200, 200).

• A cork placed in the lake -- for example, at the point (100, 100) -- might be carried around the equilibrium point (200, 200) in various different ways.
  • It could spiral around the point (200, 200) in ever tightening spirals getting closer and closer to the equilibrium point.

  • It could spiral around the equilibrium point in ever widening spirals getting further and further away.

  • It could move around the point (200, 200) in a closed loop following the same loop over and over again.

The work we have done so far cannot tell us which of these (or other possibilities) will actually occur.