Predator-Prey
Models
Part 5: The Effect of
Hunting Predators (Optional)
Suppose that predators are
removed from the population at a regular rate by hunting, say, at 5 per
year. Then the predator-prey model takes the form
dx/dt = ax -
bxy,
dy/dt = -cy +
pxy - 5,
where a, b,
c, and p are the growth and interaction parameters as before.
As in Part 4, you may use your choice of graphical representation to determine
the significance of this change.
- Modify the second differential
equation to account for hunting, and plot the solutions or trajectories
from reasonable starting values. Describe what happens. If necessary, adjust
your plot window and time scale to ensure that you have determined the
eventual fate of both species. Does the outcome make sense biologically?
- Make a different
change in the predator-prey equations to reflect a different biological
consideration. Describe the consideration. Describe the new outcome. Is
the outcome biologically reasonable?
